WEBVTT 1 00:00:40.945 --> 00:00:41.784 We can't hear you 2 00:00:41.814 --> 00:01:18.355 Eva. 3 00:01:19.379 --> 00:01:23.430 No, we can hear you now. 4 00:01:23.430 --> 00:01:27.239 Oh, thank you. Okay. Hardware. 5 00:01:27.239 --> 00:01:33.810 So this is probability that class for. 6 00:01:33.810 --> 00:01:38.189 And I'll see if I can actually. 7 00:01:38.189 --> 00:01:48.750 Share something note that 1. 8 00:01:50.099 --> 00:01:54.060 Silence. 9 00:01:56.579 --> 00:02:00.719 Silence. 10 00:02:02.159 --> 00:02:13.199 It's fine. Okay, so I have a chat window, open solitary. I can see there's snow. 11 00:02:13.199 --> 00:02:16.439 Video now 1 or 2. 12 00:02:19.949 --> 00:02:24.479 This thing. 13 00:02:40.800 --> 00:02:46.710 Side. 14 00:03:35.939 --> 00:03:42.330 Web cam, echo feedback and we can see the screen just say. 15 00:03:42.330 --> 00:03:45.569 Yeah, okay. 16 00:03:45.569 --> 00:03:49.770 Okay. 17 00:03:49.770 --> 00:03:53.699 Share browser. 18 00:03:55.830 --> 00:03:59.310 Oh, okay. 19 00:03:59.310 --> 00:04:03.389 Okay. 20 00:04:04.680 --> 00:04:08.490 I was also trying to get something up. 21 00:04:10.919 --> 00:04:24.720 As a it was at later. Okay. 22 00:04:24.720 --> 00:04:30.059 We can't see well, I mean, why would you want to see me? Oh, okay. Interesting. 23 00:04:31.108 --> 00:04:35.699 So, if you can hear me, if you can see me what is happening today. 24 00:04:36.869 --> 00:04:40.978 1st, this is the appropriate computers. 25 00:04:40.978 --> 00:04:46.858 Um, we got all these different computer systems, and they do not talk to each other. 26 00:04:48.928 --> 00:04:54.749 Okay, 1st, we're using great scope for you to submit homeworks. 27 00:04:54.749 --> 00:05:00.269 Everyone should be in it. If you, if you added late. 28 00:05:00.269 --> 00:05:03.658 You might not be so if you're not in grade scope email me. 29 00:05:03.658 --> 00:05:07.139 If you're watching this, then. 30 00:05:07.139 --> 00:05:11.129 He found out about the lectures on Webex. 31 00:05:13.168 --> 00:05:19.829 Webex meet if you you should in theory, be getting an invitation every time. 32 00:05:19.829 --> 00:05:27.689 And if you're not, then tell me, and I'll add you to the list for that again, that'd be people who added late. 33 00:05:31.048 --> 00:05:37.798 Webex teams, which is now called simple webx. They just renamed at. 34 00:05:37.798 --> 00:05:47.158 Then I think I added every 1 there also. If you're not, then this is a convenient way for people to exchange messages. 35 00:05:47.158 --> 00:05:54.059 And so on and LMS, you automatically added to that by the registrar. 36 00:05:54.059 --> 00:05:58.738 The only point about that is which is distributed grades with that. 37 00:05:58.738 --> 00:06:09.178 Because grade scope has no facility to compute grades and distribute them. It shows you grades for work, you submitted. 38 00:06:09.178 --> 00:06:14.069 It does not allow me to compute grades and stuff like that. 39 00:06:14.069 --> 00:06:17.939 And this blog, you should be reading that. 40 00:06:19.288 --> 00:06:27.629 Saul various computer systems. Okay so this is a course in engineering probability. 41 00:06:27.629 --> 00:06:30.869 It does have applications to the real world. 42 00:06:30.869 --> 00:06:35.129 And here said another 1, I meant told you what the MIT students. 43 00:06:35.129 --> 00:06:38.189 Last time. 44 00:06:38.189 --> 00:06:41.399 There's another 1 we will. 45 00:06:43.769 --> 00:06:49.403 This was a scratch off numbers game in Toronto, 46 00:06:49.403 --> 00:06:54.504 you'd scratch and there was a statistician whose GE, 47 00:06:54.533 --> 00:07:05.454 day job was designing experiments for mining companies where the mining company they sample the rock by drilling a hole and looking at the how good the, 48 00:07:05.454 --> 00:07:09.834 or is and that samples expensive to do you've got to drill a hole and so on. 49 00:07:10.139 --> 00:07:17.759 And then they decide that if this appears, this is rich enough, they then extend the mind there. 50 00:07:17.759 --> 00:07:21.449 And his day job was analyzing. 51 00:07:21.449 --> 00:07:25.259 Designing and analyzing these experiments. 52 00:07:25.259 --> 00:07:39.598 And he noticed he found a way to find out the interior lottery commission was using the same mathematics. This is techniques. So he got it. So he could look at an unscratched off ticket. 53 00:07:39.598 --> 00:07:46.889 And most of the time it would be a win or a loss. There's a long article and wire just a summary here. 54 00:07:46.889 --> 00:07:52.829 The story and Wired is that the 1st time he wrote terrible water in gaming and ignored him. 55 00:07:53.274 --> 00:08:08.064 The 2nd time he wrote them again and sent them 2 bundles of tickets that had not been scratched off. And the 1st family said were probably losers. And the 2nd bundle were probably winners. And the story goes onto the next day they cancel the interior lottery gaming. 56 00:08:08.064 --> 00:08:09.053 Cancel the game. 57 00:08:09.418 --> 00:08:23.189 If you wonder how this could work at that time, apparently the convenience stories would let customers look at the cards before deciding whether or not to buy them. And this is a little tricky had mentally. Okay. Real world. 58 00:08:23.189 --> 00:08:33.658 Real World probability. Well, also the obvious question for the statistician. Geez. Found a way to. 59 00:08:33.658 --> 00:08:42.328 You know, when at the scratch off tic, TAC toe game? Well, why did he tell you? Why didn't he just use it himself? 60 00:08:42.328 --> 00:08:47.519 Well, his answer was that he was very well paid on his day job. 61 00:08:47.519 --> 00:08:50.519 And if he exploited. 62 00:08:50.519 --> 00:09:02.188 Just look at a car, do some mental calculations decide whether or not he wants to buy the card wants to buy that. I don't put out a dollar or something. And if you went and Siemens, I don't know a couple of dollars. 63 00:09:02.188 --> 00:09:05.759 And you work it out a tolerable prowl or his day child paid more. 64 00:09:05.759 --> 00:09:15.389 So, okay, back to stuff in the course to give you techniques that who knows 1 of these years, you might use. 65 00:09:15.389 --> 00:09:21.208 And we're talking about counting techniques some. 66 00:09:22.528 --> 00:09:32.849 And so I'm showing you some stuff here that I'm referring to stuff on the on Garcia, enrich, or add key, has his videos and my. 67 00:09:32.849 --> 00:09:41.009 Teaching technique as you look at these different things and you see the same topic presented from different directions. 68 00:09:41.009 --> 00:09:44.278 And this will give you a better chance. 69 00:09:44.278 --> 00:09:47.308 Of a better chance of understanding it. 70 00:09:47.308 --> 00:09:53.308 And let me actually get my little coin. 71 00:09:53.308 --> 00:09:58.859 And. 72 00:09:58.859 --> 00:10:06.389 Okay, switch over to the. 73 00:10:06.389 --> 00:10:09.839 Over cam and hope it doesn't crash everything. 74 00:10:16.528 --> 00:10:19.948 And I'll try to share everything together. 75 00:10:19.948 --> 00:10:23.639 This and see what we get. 76 00:10:26.188 --> 00:10:31.678 Silence. 77 00:12:05.399 --> 00:12:15.749 I don't know who can hear me now, but my attempt to share my complete screen locked up my computer. So this will take a minute or 2. sorry you about this. 78 00:15:51.178 --> 00:15:57.448 Oh, hey. 79 00:15:57.448 --> 00:16:01.708 So. 80 00:16:01.708 --> 00:16:08.818 Back again maybe and. 81 00:16:27.028 --> 00:16:33.328 So, okay, the other. 82 00:16:33.328 --> 00:16:37.318 So just not. 83 00:16:37.318 --> 00:16:50.009 Silence. 84 00:17:05.219 --> 00:17:16.648 Okay. 85 00:17:16.648 --> 00:17:21.568 So. 86 00:17:21.568 --> 00:17:27.689 What happened is I tried to share the whole screen and it. 87 00:17:29.249 --> 00:17:36.659 And locked up my whole machine, so, and trying to connect another machine, started the feedback loop. So now. 88 00:17:36.659 --> 00:17:40.858 Maybe we can try something that's share. 89 00:17:43.348 --> 00:17:47.338 See, what we can do here. 90 00:17:59.098 --> 00:18:02.669 We have a can. 91 00:18:21.479 --> 00:18:24.778 Now, it says it can't share my content. 92 00:18:26.759 --> 00:18:30.898 This is getting silly. 93 00:23:39.449 --> 00:23:46.558 Silence. 94 00:23:48.028 --> 00:23:51.028 Okay, so. 95 00:23:52.828 --> 00:23:58.558 What I finally did is I switched to a different laptop, which appears to be more reliable, even though it's and. 96 00:23:58.558 --> 00:24:02.009 Older laptop, so. 97 00:24:05.068 --> 00:24:15.028 Question is. 98 00:24:19.828 --> 00:24:25.528 Great sorry about that. The funny thing is the older laptop is more reliable. 99 00:24:25.528 --> 00:24:30.509 Than the newer laptop go figure in any case. So. 100 00:24:30.509 --> 00:24:35.128 But we're talking about permutations and so on. 101 00:24:39.808 --> 00:24:44.249 And let me show you, by example so. 102 00:24:44.249 --> 00:24:49.798 We have. 103 00:24:49.798 --> 00:24:55.348 Of course, I'm not showing the webcam now. 104 00:24:58.048 --> 00:25:01.828 Not connect to display well. 105 00:25:01.828 --> 00:25:05.398 I'll be talking about it then. 106 00:25:05.398 --> 00:25:08.578 I give up I tried on 2 different laptops. 107 00:25:13.288 --> 00:25:18.989 We'll look at what I've typed we'll look at what I've typed in, I was trying to write notes on the. 108 00:25:18.989 --> 00:25:22.648 For the hover cam, but when I try to connect the. 109 00:25:22.648 --> 00:25:27.419 Hover cam to 2 different laptops. The thing hangs up. 110 00:25:27.419 --> 00:25:33.388 So, I'll give it 1 more attempt and then see. 111 00:25:33.388 --> 00:25:36.778 Oh, just a SEC and this may work. 112 00:25:40.409 --> 00:25:49.679 It may also lock things up, but we'll see. 113 00:25:49.679 --> 00:25:53.159 Hey, wow. 114 00:25:53.159 --> 00:25:58.769 We actually have something that works, so okay. 115 00:25:58.769 --> 00:26:04.588 Silence. 116 00:26:04.588 --> 00:26:07.679 Good how are you going. 117 00:26:10.108 --> 00:26:19.288 Silence. 118 00:26:19.288 --> 00:26:24.449 So this is here for. 119 00:26:24.449 --> 00:26:28.949 Silence. 120 00:26:28.949 --> 00:26:33.449 So, we have some coins here and let me bring up this again. 121 00:26:37.648 --> 00:26:42.689 So we have an earn within balls here. Let me bring up the chat window also. 122 00:26:42.689 --> 00:26:47.848 Well, I can't figure up everything all at the same time is the problem. 123 00:26:47.848 --> 00:26:55.019 So, we have maybe they're different. Maybe they're not. So, the question is that. 124 00:26:55.019 --> 00:26:58.979 I mean, that's suppose that I have. 125 00:27:00.148 --> 00:27:05.669 That suppose that I have, I don't know. 126 00:27:05.669 --> 00:27:10.558 3 quarters and. 127 00:27:10.558 --> 00:27:14.249 And 2 times or something. 128 00:27:14.249 --> 00:27:17.729 And now we have a question is. 129 00:27:17.729 --> 00:27:21.749 If I draw. 130 00:27:21.749 --> 00:27:24.959 You know, I might say. 131 00:27:28.048 --> 00:27:34.499 Here are some coins are different, some clients or not and maybe I say I draw. 132 00:27:34.499 --> 00:27:37.858 3 coins without replacement, let's say. 133 00:27:37.858 --> 00:27:51.449 Silence. 134 00:27:58.558 --> 00:28:01.949 Right. 135 00:28:03.538 --> 00:28:11.699 2nd, here. 136 00:28:11.699 --> 00:28:15.568 Silence. 137 00:28:18.179 --> 00:28:24.598 And I've got something like. 138 00:28:24.598 --> 00:28:30.148 I've got something here and I've got to say 3 quarters. 139 00:28:32.368 --> 00:28:35.729 Plus, um. 140 00:28:36.898 --> 00:28:41.969 Silence. 141 00:28:41.969 --> 00:28:46.348 Us 2 times. Okay so. 142 00:28:46.348 --> 00:28:54.028 Without replacement 3 quarters. 143 00:28:55.949 --> 00:29:00.179 Not possible. 144 00:29:00.179 --> 00:29:03.778 Okay, without replacement with replacement. 145 00:29:07.558 --> 00:29:11.219 Yes, yes, it's possible. 146 00:29:12.449 --> 00:29:17.548 Okay, just to motivate things. Okay so going over here. 147 00:29:17.548 --> 00:29:25.469 And so replacement is we put the ball back after it. 148 00:29:25.469 --> 00:29:29.969 Okay, so I've got some examples here also. 149 00:29:31.259 --> 00:29:36.328 Class of students let me bring this up. 150 00:29:37.739 --> 00:29:41.159 Related things. 151 00:29:41.159 --> 00:29:44.159 Silence. 152 00:29:44.159 --> 00:29:48.388 Silence. 153 00:29:48.388 --> 00:29:54.148 Silence. 154 00:29:55.229 --> 00:29:59.699 Okay, and. 155 00:30:03.179 --> 00:30:07.288 Silence. 156 00:30:07.288 --> 00:30:10.439 Only regroup membership managers. Okay. 157 00:30:12.388 --> 00:30:17.338 Okay, order drawn. 158 00:30:17.338 --> 00:30:21.328 Okay, so how we would do something like that, let's say. 159 00:30:22.618 --> 00:30:30.058 Um, well, let me pull up the chat window again, just so I can see if there are questions. 160 00:30:30.058 --> 00:30:37.169 Okay, okay. 161 00:30:37.169 --> 00:30:41.159 You're right, make this dimes. 162 00:30:41.159 --> 00:30:45.058 Thank you, Nicholas, you get a point. 163 00:30:45.058 --> 00:30:48.898 You're awake. Okay. 164 00:30:48.898 --> 00:30:53.489 Okay, so how would we, let's say 12 students into 2 groups of 6. 165 00:30:53.489 --> 00:30:56.669 Where we don't care about. 166 00:30:56.669 --> 00:31:02.128 The order if we think about that, how how would we do something. 167 00:31:02.128 --> 00:31:09.419 Like that, um, well, Here's an idea. 168 00:31:10.469 --> 00:31:24.328 If you're wondering why I got the had the quarter off at the top here is to try and force the camera out of focus the focus. But now that I've got some text focused on that. Okay. 169 00:31:26.398 --> 00:31:30.148 So, 12 ways. 170 00:31:30.148 --> 00:31:43.888 1st student, then 11 ways to fix a 2nd, 10 ways to fix the 3rd, 9 ways to pick the 4th, 8 ways to pick the 5th 7 ways to pick the 6. 171 00:31:43.888 --> 00:31:49.348 And that's it thing just locked up on me again. 172 00:31:49.348 --> 00:31:55.048 Okay. 173 00:32:05.189 --> 00:32:18.209 Of our catalog. 174 00:32:20.038 --> 00:32:27.419 Silence. 175 00:32:27.419 --> 00:32:32.638 Silence. 176 00:32:38.999 --> 00:32:45.028 Silence. 177 00:32:47.159 --> 00:32:52.558 Silence. 178 00:32:59.459 --> 00:33:05.939 Silence. 179 00:33:05.939 --> 00:35:05.938 Silence. 180 00:35:08.813 --> 00:35:33.414 Am 181 00:35:33.414 --> 00:35:34.583 I right? 182 00:37:51.088 --> 00:37:58.559 Okay, does this work? Okay. Oh, I'm using the. 183 00:37:58.559 --> 00:38:06.599 I mean, I'm using audio from my phone and video from the hover camp. Yeah, yeah, yeah. Yeah. 184 00:38:06.599 --> 00:38:10.858 So, where we were. 185 00:38:10.858 --> 00:38:14.760 Was learning about drawing. 186 00:38:14.760 --> 00:38:27.329 And from my nursing, and my 1st example with numbers was, this is selection without replacement and we don't care about the order. I assume that we have 12 students. 187 00:38:27.329 --> 00:38:31.230 That we are dividing into 2 groups. 188 00:38:31.230 --> 00:38:38.639 And therefore, the number of ways we can do it, and we don't care about. 189 00:38:38.639 --> 00:38:48.090 And those say a good 1 and a group 2, we don't care about the order. The students who are selected for group 1. we just care about. 190 00:38:48.090 --> 00:38:51.269 Who's in group 1 now. 191 00:38:51.269 --> 00:38:54.480 How do we do that? Well. 192 00:38:54.480 --> 00:39:05.699 What I'm going to do is select 12 students for group 1 and 6 students. I'm sorry for group 1 and the other 6 will be in group 2. 193 00:39:05.699 --> 00:39:09.119 So. 194 00:39:09.534 --> 00:39:21.804 So there are 12 ways I can pick the 1st student to go into group 1 now there's 11 students left. So I pick 1 of those 11 students, throw him or her into group. 1 is 10 students remaining. 195 00:39:21.804 --> 00:39:28.855 I pick 1 of those 10 any 1 of those 10 than any 1 of those 9, 8 and 7. so what I've got in here. 196 00:39:29.130 --> 00:39:35.070 Is 12 times 11 times 10 times 9 times 8 times 7. 197 00:39:35.070 --> 00:39:40.289 Now, however, this way the order matters so. 198 00:39:40.289 --> 00:39:44.610 What I have to do now is divide. 199 00:39:44.610 --> 00:39:52.409 Because this here will count it differently. If I pick the same students in a different order. 200 00:39:52.409 --> 00:39:56.039 So, I have to divide by the number of. 201 00:39:56.039 --> 00:39:59.309 Different ways I could have picked each group. 202 00:39:59.309 --> 00:40:02.730 Let me show you what I mean, here. 203 00:40:21.449 --> 00:40:25.079 Of the same set, so. 204 00:40:26.369 --> 00:40:31.170 That's correct. 205 00:40:33.840 --> 00:40:38.010 Let me show you what I mean, I'm going to do it a simpler way. Let's say. 206 00:40:46.500 --> 00:40:51.510 Into a simpler case, and equals 4 students. 207 00:40:54.150 --> 00:40:57.300 Okay, cause 2 and 1st group. 208 00:40:59.159 --> 00:41:03.449 Hey, see see. Okay so. 209 00:41:04.769 --> 00:41:09.780 So, what I'm picking is I could pick a. 210 00:41:09.780 --> 00:41:17.639 And then B, or I could pick a, and then C or a, and D or B or B and a. 211 00:41:17.639 --> 00:41:23.280 B, and C. D and D. C and a and B. 212 00:41:23.280 --> 00:41:30.210 C and D, but the trouble is that I've picked, for example. 213 00:41:30.210 --> 00:41:34.800 I got a and B, and I thought also be a. 214 00:41:34.800 --> 00:41:41.429 And I don't want to count them separately so what I do, so this was the total here. 215 00:41:41.429 --> 00:41:44.460 Of 4 times 3 equals 12. 216 00:41:44.460 --> 00:41:52.469 Now, but each group. 217 00:41:55.170 --> 00:42:02.039 It was listed twice, say a be. 218 00:42:02.039 --> 00:42:07.170 And be a, so I divide. 219 00:42:08.909 --> 00:42:16.079 By too, and so the result is 12 over 2 equal 6. 220 00:42:16.079 --> 00:42:20.969 And it's a B. A. C. A. T. 221 00:42:20.969 --> 00:42:25.199 B. C. D. E. E. C. D. 222 00:42:25.199 --> 00:42:28.199 Okay, so. 223 00:42:28.199 --> 00:42:31.260 In order to. 224 00:42:38.309 --> 00:42:47.489 Um, yeah. 225 00:42:47.489 --> 00:42:55.050 Okay, how about the correct for that? Right? So that what we have is. 226 00:42:56.190 --> 00:42:59.429 We have, um. 227 00:42:59.429 --> 00:43:03.420 For the 2 case, it is. 228 00:43:05.429 --> 00:43:11.340 It's 4 choose 2 and that's 4 factorial over 2 factor to factorial. 229 00:43:11.340 --> 00:43:17.639 It's just 24 or 2. 2 equals 6. yeah the bigger case is. 230 00:43:20.010 --> 00:43:25.019 The number of ways, when I said 12 times, 11 times, 10, and so on. 231 00:43:26.159 --> 00:43:30.809 Up to 7, that would be 12 factorial or 6 factorial. 232 00:43:30.809 --> 00:43:39.030 That's big there that picked each group. 233 00:43:42.090 --> 00:43:46.739 K. factorial times factorial ways. 234 00:43:47.760 --> 00:43:54.929 So the final answer is, is. 235 00:43:54.929 --> 00:43:58.710 Factorial over 6 sector 6 editorials so. 236 00:43:58.710 --> 00:44:03.539 In fact, chore over K editorial and minus K factorial. 237 00:44:03.539 --> 00:44:07.619 Equals and choose K, it's called and. 238 00:44:07.619 --> 00:44:12.360 Choose hey okay. 239 00:44:12.360 --> 00:44:17.789 So some of you are ahead are ahead of me, but not everyone. That's why I'm taking it slowly. 240 00:44:17.789 --> 00:44:21.360 Okay, pack up to the. 241 00:44:21.360 --> 00:44:25.019 Here back up to. 242 00:44:26.579 --> 00:44:31.230 Here here. 243 00:44:34.559 --> 00:44:41.610 Okay, now, if I look at the B, here. 244 00:44:41.610 --> 00:44:45.030 88 students 4 teams of. 245 00:44:47.130 --> 00:44:51.119 Okay, each well. 246 00:44:51.119 --> 00:44:56.280 This would be page. 247 00:44:56.280 --> 00:45:00.750 Or this is say the example to. 248 00:45:02.039 --> 00:45:05.130 B, well. 249 00:45:09.090 --> 00:45:12.179 Okay, so. 250 00:45:12.179 --> 00:45:15.389 We'll pick the 1st, team of 6 students. 251 00:45:15.389 --> 00:45:19.559 The number of ways, so the 1st team will be. 252 00:45:19.559 --> 00:45:25.320 Ov, 8 choose 6 actually. 253 00:45:28.440 --> 00:45:31.650 And pick a team of 6 and. 254 00:45:31.650 --> 00:45:36.449 Since that are posting on the chat thing. 255 00:45:36.449 --> 00:45:43.739 No, okay. And then that leaves 70, 82 so. 256 00:45:43.739 --> 00:45:49.530 82, 6 for the 2nd, 176 6 for the 3rd. 257 00:45:49.530 --> 00:45:53.610 And 76 for the 4th. 258 00:45:53.610 --> 00:45:56.880 And that will net out as. 259 00:45:56.880 --> 00:46:03.210 A factorial over 6 secretarial 6, actuarial 6, secretarial factorial. 260 00:46:10.344 --> 00:47:23.454 Eva. 261 00:47:27.300 --> 00:47:39.690 Good okay. 262 00:47:40.824 --> 00:47:55.045 So, okay, this is a reason for in person classes. Okay if the hardware works better. 263 00:47:55.380 --> 00:47:59.190 Okay, so where where are we, we were. 264 00:47:59.190 --> 00:48:04.380 Picking 4 teams of 6 students from a class of 88, and we are getting something. 265 00:48:04.380 --> 00:48:07.800 Like that so it's selection without replacement. 266 00:48:07.800 --> 00:48:19.530 Everyone knows what factorial is. I assume if you don't then tell me. 267 00:48:19.530 --> 00:48:23.550 Good, thank you. Nicholas. 268 00:48:25.500 --> 00:48:32.849 So reason to go back to Blackboard all our old classrooms that have Blackboard. Only trouble is to chalk is messy. 269 00:48:32.849 --> 00:48:42.510 Okay, 5 cards from a deck. What's the probability that they're all from? The same suit? 270 00:48:44.130 --> 00:48:49.829 How could we do that? Okay. 271 00:48:51.090 --> 00:48:56.130 Here's 1 way the 1st card. 272 00:48:56.130 --> 00:49:00.809 Doesn't matter what. 273 00:49:02.579 --> 00:49:08.760 If you 1 last 2nd card has to be from the same suit. 274 00:49:18.960 --> 00:49:23.550 As 12 of them 3rd card da, there's 11 of them. 275 00:49:23.550 --> 00:49:28.679 4th card done in about this 10 of them this car got under. There's 9 of them. 276 00:49:28.679 --> 00:49:33.869 To the number of ways, 8 walls. 277 00:49:34.889 --> 00:49:39.269 12 factorial over 8. factorial actually. 278 00:49:39.269 --> 00:49:42.840 Of picking 5 cards. 279 00:49:44.099 --> 00:49:48.389 And then also. 280 00:49:48.389 --> 00:49:56.610 Order matters, we can't it doesn't matter. 281 00:49:56.610 --> 00:50:00.179 Yes, we can see what you're writing. 282 00:50:02.099 --> 00:50:07.619 Now, you cannot see that. Now, I'm not sharing the screen open. 283 00:50:07.619 --> 00:50:11.010 Thank you. 284 00:50:28.710 --> 00:50:35.489 See, anything now, thank you. Okay. 285 00:50:35.489 --> 00:50:40.500 Okay, I'm taking votes now and what will fail next. 286 00:50:43.860 --> 00:50:50.940 Only thing is, is I don't care if the power grid fails, because I got my Tesla power walls in the garage. So. 287 00:50:50.940 --> 00:50:54.659 So, the problem was so. 288 00:50:54.659 --> 00:50:59.550 We're picking 5 cards out of the 50 cards. 289 00:50:59.550 --> 00:51:08.280 Deck nothing funny about the deck. The number of ways I could pick 5 cards from the 1st suit as well. 290 00:51:08.280 --> 00:51:14.070 Over 8 factorial, but the order matters. So each particular 5 card. 291 00:51:15.630 --> 00:51:21.329 And got picked by factorial ways. So if the order. 292 00:51:21.329 --> 00:51:29.699 It doesn't matter then it's going to be. 293 00:51:29.699 --> 00:51:33.989 Factorial over. 294 00:51:33.989 --> 00:51:40.260 Hi, factorial ways. So what's the probability? 295 00:51:43.380 --> 00:51:48.150 Well, we could just look at the number of ways up there and look at the number of different. 296 00:51:50.429 --> 00:51:54.210 Page 5. 297 00:51:54.210 --> 00:52:05.880 To calculate probability of ability. 298 00:52:08.820 --> 00:52:15.599 Oh, we could look at the order you use the ordered numbers maybe might be easier. 299 00:52:19.139 --> 00:52:26.340 You see, order dancer, the number of hands. 300 00:52:28.409 --> 00:52:33.989 Was the. 301 00:52:36.239 --> 00:52:40.800 Number of hands not required. 302 00:52:41.909 --> 00:52:48.719 To be in the same in the same. 303 00:52:49.800 --> 00:52:54.119 Would be, um. 304 00:52:54.119 --> 00:52:57.780 52 factorial and 52 minus 5. 305 00:52:57.780 --> 00:53:05.730 47 factorial, and I pick any 1 of the 52 cards, and any 1 of the remaining 51. 306 00:53:05.730 --> 00:53:10.710 So, the probability is going to be 1 over 2. 307 00:53:10.710 --> 00:53:16.199 Which is, um. 308 00:53:16.199 --> 00:53:20.699 Or this is 1 and just this 2 over. 309 00:53:26.099 --> 00:53:30.570 And I could perhaps simplify that, but. 310 00:53:30.570 --> 00:53:35.789 Oh, okay. 311 00:53:38.849 --> 00:53:43.170 Back to so there. 312 00:53:47.429 --> 00:53:51.179 If I go back to that 1 of picking. 313 00:53:51.179 --> 00:54:00.389 Say, well, students where the order does matter, then we don't divide by the number of ways of getting same sets. We're not dividing by a. 314 00:54:00.389 --> 00:54:04.050 So now. 315 00:54:04.050 --> 00:54:08.699 My example E, here now, this starts getting economically interesting. 316 00:54:08.699 --> 00:54:15.780 You're running a factory. Okay and you produced a 100 widgets. 317 00:54:15.780 --> 00:54:25.559 And maybe, you know, we're going to do this 2 ways. The easy 1 is we know that 10 widgets are bad. Let's say. 318 00:54:25.559 --> 00:54:28.590 And before we'll try to compute that. 319 00:54:28.590 --> 00:54:32.039 So, we pick 5 widgets. 320 00:54:32.039 --> 00:54:37.679 And what's the probability that of the 5 points? We happen to pick that? None are bad. 321 00:54:37.679 --> 00:54:43.889 Now, some context here picking and testing the widgets may cost some time and money. 322 00:54:43.889 --> 00:54:49.889 And it's also possible that testing the way it just might destroy them. It might be destructive testing. 323 00:54:49.889 --> 00:54:57.420 So, what we want to do is we want to know how much confidence we have. 324 00:54:57.420 --> 00:55:01.380 Um, you know, that. 325 00:55:01.380 --> 00:55:05.159 You know, we picked we pick a sample of widgets and. 326 00:55:05.159 --> 00:55:10.949 If we know that 10% of them are bad, then what's the probability that our in our sample. 327 00:55:10.949 --> 00:55:15.300 None are bad or all 5 are bad or something like that. 328 00:55:15.300 --> 00:55:19.349 Let's look at that. 329 00:55:24.750 --> 00:55:30.000 Oh, by the way before I go on where I put my handwritten notes, I'll show you. 330 00:55:30.000 --> 00:55:36.539 Back up to here at the top. 331 00:55:36.539 --> 00:55:40.800 There is a tab that says files and. 332 00:55:40.800 --> 00:55:47.699 If you look here, see handwritten handwritten 3, right up there. 333 00:55:47.699 --> 00:55:54.599 That was him last time. Oh, God. 334 00:55:54.599 --> 00:56:06.719 What else is going to go wrong? 335 00:56:06.719 --> 00:56:12.179 Okay, I know what happened here. Ignore this attempt just call you. 336 00:56:12.179 --> 00:56:18.059 Or the handwritten notes are later this evening if you go care. 337 00:56:18.059 --> 00:56:21.329 And it will show you the handwritten notes. 338 00:56:22.500 --> 00:56:27.900 Like, there is still 1 from class 2 if there was nothing handwritten from class 1. 339 00:56:27.900 --> 00:56:31.469 Okay, if you're curious what happened here. 340 00:56:33.119 --> 00:56:43.050 I use get get annex to do backups of large files and handwritten notes. Just aren't large files. 341 00:56:44.789 --> 00:56:53.250 So, with get annex, it doesn't automatically put a copy of the file everywhere. I have to tell it the, and because the files are big. 342 00:56:53.250 --> 00:57:00.900 And I have to tell us to put a copy of this large file on the web server. What's there? Right now is just a link. 343 00:57:00.900 --> 00:57:09.719 Nonexistent large file. Okay. We are back at economic problem. 344 00:57:09.719 --> 00:57:14.519 Of the there. 345 00:57:14.519 --> 00:57:20.039 See, if there's any questions. 346 00:57:24.119 --> 00:57:28.199 How do we know if there are 1 time use. 347 00:57:29.610 --> 00:57:32.820 How I explained, I got 1 half again. 348 00:57:39.210 --> 00:57:42.989 Or so 1, half. 349 00:57:45.449 --> 00:57:52.199 Mohammed, could you tell me which is it was it on page? 5 here? 350 00:57:52.199 --> 00:57:56.340 On that page for there. Okay. 351 00:57:56.340 --> 00:58:00.059 Oh, this I'm sorry, that's not 1 half. 352 00:58:00.059 --> 00:58:06.480 That's a equation 1. 353 00:58:06.480 --> 00:58:11.730 You guy, I'm sorry about that. It's not 1 half. 354 00:58:11.730 --> 00:58:15.059 Okay, thank you. So. 355 00:58:15.059 --> 00:58:19.409 Yeah, well. 356 00:58:20.639 --> 00:58:26.280 Okay. 357 00:58:35.099 --> 00:58:43.469 Okay, there you go. 358 00:58:44.519 --> 00:58:49.769 Okay, how did author 1 time use. 359 00:58:49.769 --> 00:58:57.929 You have to be told oh, basically. 360 00:58:59.250 --> 00:59:04.050 So, if we're drawing cards from a. 361 00:59:04.050 --> 00:59:09.085 Deck the Isis page is a 1 time use, 362 00:59:09.414 --> 00:59:10.824 you draw 1 a space, 363 00:59:11.125 --> 00:59:17.815 and they probably are not going to draw a 2nd day suspect because you are the other people around the table got to get exceedingly annoyed, 364 00:59:18.204 --> 00:59:22.494 and we might get a chance to calculate vital statistics like your life expectancy. 365 00:59:23.005 --> 00:59:24.114 Okay. Now. 366 00:59:27.510 --> 00:59:33.809 So, back to, or do we have it here? 367 00:59:35.159 --> 00:59:41.099 Widgets okay, so this is economically interesting because. 368 00:59:41.099 --> 00:59:47.369 Test costs money, but you want to have some guarantees for customers. 369 00:59:47.369 --> 00:59:51.900 Okay um, so. 370 00:59:57.599 --> 01:00:02.219 Pick 5 good widgets. 371 01:00:04.199 --> 01:00:07.409 So, remember, we have 100 widgets. 372 01:00:07.409 --> 01:00:10.920 And they are. 373 01:00:10.920 --> 01:00:18.449 10 bad. Okay. I'm just trying with for widget. Okay. Now. 374 01:00:18.449 --> 01:00:25.800 To pick 5 good ones. Well, it would be 90 times. 89 has 88. 375 01:00:25.800 --> 01:00:30.179 7 times 86 it was 100 vectorial over. 376 01:00:30.179 --> 01:00:33.329 I think a number of ways to pick it. 377 01:00:33.329 --> 01:00:38.519 Okay um, good pick. 378 01:00:43.889 --> 01:00:46.920 90 sanctuary over 85. thanks for. 379 01:00:46.920 --> 01:00:51.900 Pick 100 widgets don't care. 380 01:00:51.900 --> 01:00:56.519 Would be 100 factorial over a 95 back. 381 01:00:57.840 --> 01:01:04.139 So, the prob that all 5. 382 01:01:04.139 --> 01:01:07.650 Are good is. 383 01:01:07.650 --> 01:01:11.070 Now, any factorial for 85 factorial. 384 01:01:11.070 --> 01:01:14.670 Okay. 385 01:01:16.199 --> 01:01:19.920 So, how you would calculate that. 386 01:01:21.630 --> 01:01:36.210 A good double for you. Well, there are ways to simplify that, so you could not just put 100 factorial into your calculator. It will overflow. The numbers will be very large, but. 387 01:01:38.070 --> 01:01:52.469 Well, things cancel out like this here, instead of saying, 90 factorial and 85 or you just, you just compute that product and there. Okay. So that's the probability that you happen to pick all 5. 388 01:01:52.469 --> 01:02:05.519 Good widget. Exactly. 389 01:02:07.320 --> 01:02:13.170 1 bag widget. Okay. Um. 390 01:02:17.519 --> 01:02:21.090 What's different ways we could do it now. Okay. 391 01:02:25.320 --> 01:02:34.019 Here's the simple way. It's not the most sophisticated, but it's easiest to understand. 392 01:02:35.820 --> 01:02:41.340 Easy not fancy. 393 01:02:43.739 --> 01:02:49.500 Well, the, the 5 cases. 394 01:02:52.949 --> 01:02:59.280 Bad widget is the 1st or the 2nd or the 3rd or. 395 01:02:59.280 --> 01:03:07.829 Or if there's something the bad widget is the 1st, then it's got. 396 01:03:07.829 --> 01:03:14.969 10 cases, and then the 2nd, 1, you draw could be any 1 of the 90 good ones. 397 01:03:14.969 --> 01:03:19.769 And then the 3rd, 1 is any 1 of the 89 good ones. Ata. 398 01:03:19.769 --> 01:03:22.949 87 the 2nd example. 399 01:03:22.949 --> 01:03:30.630 Is a good and then a bad and 3 goods. The good 1 is any 1 of 90 bad 1 is any 1 of 10. 400 01:03:30.630 --> 01:03:34.739 And then the 2nd, good 189 8. 401 01:03:34.739 --> 01:03:37.889 7, and then you're noticing a pattern here. 402 01:03:37.889 --> 01:03:43.800 And you can calculate the number of. 403 01:03:43.800 --> 01:03:50.309 Ways you can pick you'll get exactly 1 bad widget. 404 01:03:50.309 --> 01:03:53.309 Page 7. 405 01:03:53.309 --> 01:03:57.000 So. 406 01:03:58.230 --> 01:04:05.010 It's going to be. 407 01:04:10.170 --> 01:04:14.909 Exactly. 1 bag widget. 408 01:04:16.019 --> 01:04:21.119 That's going to be 5 times. 409 01:04:23.579 --> 01:04:28.380 5 times 10 times, um. 410 01:04:28.380 --> 01:04:33.780 Factorial over 86 factorial so. 411 01:04:35.789 --> 01:04:41.909 And then you divided by the number of ways and again, this way order matters up here. 412 01:04:41.909 --> 01:04:47.039 So, if we did it without order mattering, then it would make it a little sense here. So. 413 01:04:48.750 --> 01:04:56.550 Yeah, okay now. 414 01:04:57.630 --> 01:05:00.929 So, but the real. 415 01:05:02.880 --> 01:05:14.699 Uh, the real world problem not no. 416 01:05:15.840 --> 01:05:20.099 Number of bad widgets. Okay. 417 01:05:22.590 --> 01:05:25.920 You pick 5. 418 01:05:27.599 --> 01:05:34.590 See, 0T bad, you know what does that tell you. 419 01:05:40.739 --> 01:05:45.599 Or you see 1 bad or whatever. Okay. 420 01:05:45.599 --> 01:05:49.800 So, if you pick. 421 01:05:49.800 --> 01:05:56.369 I've, you know, you've got 100 awaited. You don't know how many are bad. You pick 5, you happen to see no bad. 422 01:05:57.900 --> 01:06:02.940 What does that tell you about the original set? Now? That gets interesting. Okay. 423 01:06:03.960 --> 01:06:07.949 So another example. 424 01:06:07.949 --> 01:06:11.849 Interesting thing called approval voting. 425 01:06:11.849 --> 01:06:18.900 Give you a real world example that choose the I, Tripoli, when they elect for president. 426 01:06:20.219 --> 01:06:29.820 What happened a few decades ago in the Tripoli? What have you guys? Tripoli would have the board would nominate 2 official candidates. 427 01:06:29.965 --> 01:06:30.534 And 428 01:06:30.565 --> 01:07:32.065 Eva. 429 01:07:37.889 --> 01:07:45.840 Thank you Thomas. Okay. I have managed to confuse. 430 01:07:45.840 --> 01:07:52.409 Andrew, okay, turn on your speak, turn on your sound if you want and. 431 01:07:52.409 --> 01:08:03.420 Ask, what's the question? Are you not. 432 01:08:07.530 --> 01:08:16.770 Okay, you don't know what you don't know. 433 01:08:16.770 --> 01:08:24.750 Okay, thank. 434 01:08:33.270 --> 01:08:37.229 Okay, well I'll think about that and then. 435 01:08:38.369 --> 01:08:41.460 86. 436 01:08:41.460 --> 01:08:44.939 Here, um. 437 01:08:46.050 --> 01:08:59.670 Sure. Okay. So the problem was this here. 438 01:09:06.600 --> 01:09:11.159 So, we want. 439 01:09:11.159 --> 01:09:23.310 To we have 100 widgets we know that 99 of them are good and 10 of them are bad. Just don't say how we know it, but we know it. 440 01:09:23.310 --> 01:09:27.720 We took 5 of them at random and. 441 01:09:27.720 --> 01:09:30.930 Every time we fix 5, we're going to see something different. 442 01:09:30.930 --> 01:09:38.520 But I want to know how we could end up with exactly 1 of those 5 being bad. And 4 of those 5. 443 01:09:38.520 --> 01:09:42.600 Being good. So how many ways can that happen? 444 01:09:42.600 --> 01:09:47.250 And then from there, what's the probability? Well. 445 01:09:47.250 --> 01:09:52.739 I just did it nice and simply here, it's hard to think of sophisticated ways. 446 01:09:55.170 --> 01:09:58.770 How could we have? 1 bad and 4 good widgets. 447 01:09:58.770 --> 01:10:03.180 Maybe the bad, which is the 1st 1 we pick. It's not maybe it's the 2nd. 448 01:10:03.180 --> 01:10:09.359 If not, maybe it's the 3rd, if not, maybe it's the 4th and if it's none of those, it has to be the. 449 01:10:09.359 --> 01:10:15.659 Okay, so let's take the 1st case. That bandwidth is the 1st 1 we pick. 450 01:10:15.659 --> 01:10:20.819 Is 10 bad widget so there's 1010 that we could pick there. 451 01:10:20.819 --> 01:10:27.119 Or the 1st time now, the next 4 all have to be good. There's 90 good widgets. 452 01:10:27.119 --> 01:10:39.569 And the number of ways we can do that, or I'm not correcting if I don't care about sorry, just saying order matters at the moment is 90. the 1st good. 1 I draw is 90 choices is 89 choices. 453 01:10:39.569 --> 01:10:44.489 Um, for the 2nd widget, because it's only 89 good which times? 88 times 87. 454 01:10:44.489 --> 01:10:49.829 That there is a number of ways to draw 5 widgets where the 1st, 1 is bad. 455 01:10:49.829 --> 01:10:58.260 And the next 4 are good now 90 times 88 times times 89 Z8 and 87 is equal to 90 factorial. 456 01:10:58.260 --> 01:11:02.819 Divided by a C6 factorial. 457 01:11:02.819 --> 01:11:07.649 That what you were asking about. 458 01:11:09.869 --> 01:11:13.590 8980 8786. 459 01:11:13.590 --> 01:11:21.479 Huh. 460 01:11:23.189 --> 01:11:35.520 Oh, this is a ways to pick 5 good wages. Okay. The ways to pick. 461 01:11:36.779 --> 01:11:40.890 5 widgets that 90, 80, 90, 87, but. 462 01:11:40.890 --> 01:11:44.520 It's 90 factorial divided by 8 6. 463 01:11:44.520 --> 01:11:47.609 That was that was so hanging you up. 464 01:11:47.609 --> 01:11:52.170 And again, 86 and so on. So that is. 465 01:11:52.170 --> 01:11:56.880 I got it right there. So, was that the problem. 466 01:11:58.170 --> 01:12:03.899 Or was it something else. 467 01:12:03.899 --> 01:12:07.199 Well, the chat. 468 01:12:10.470 --> 01:12:13.560 Good great. Okay. 469 01:12:14.850 --> 01:12:18.149 So, he's talking about approval voting. 470 01:12:18.149 --> 01:12:23.489 Let me slide the silver, so I can watch the chat window. 471 01:12:23.489 --> 01:12:33.869 Like, much my ultimate goal is I have the chat window off on a different computer, but that just. 472 01:12:33.869 --> 01:12:37.140 I've got enough things way things can fail. 473 01:12:37.140 --> 01:12:41.189 Approval voting I was going to give you an agreeable historical example. 474 01:12:41.189 --> 01:12:53.399 By Tripoli each annual election for the president of the I, Tripoli, the board would nominate 2 official candidates. 475 01:12:53.399 --> 01:12:59.550 And then any member could run by petition if he got the 1000 to get on a petition or something. 476 01:12:59.550 --> 01:13:06.329 So, there's the guy called Aaron chairs who didn't like the establishment would. 477 01:13:06.329 --> 01:13:12.420 Run by petition, and he would always lose, but he was getting more votes each time. 478 01:13:12.420 --> 01:13:16.050 And the board got worried that he would. 479 01:13:16.050 --> 01:13:22.920 That the 2 establishment candidates might split the vote and fierce might win with 35% of the vote or something. 480 01:13:23.694 --> 01:13:38.395 So, they changed the voting scheme by vote of the board to an approval system, or they would still nominate 2 official candidates. But you could vote as many for, as many candidates as you wanted. You could vote for both of them if you liked them or just. 481 01:13:38.395 --> 01:13:39.173 1 of them more. 482 01:13:39.539 --> 01:13:44.579 Vote at all or both professed or something and the idea was. 483 01:13:44.579 --> 01:13:58.979 You would vote for everyone whom you found acceptable anyone who that was called approval. So there. So what they assumed was that the people who liked the established board would pick both of their official candidates and fierce could not. 484 01:13:58.979 --> 01:14:02.939 Split the vote and win and that's in fact what happened, but that's approval voting. 485 01:14:04.289 --> 01:14:09.720 So you might, you know, the question here is how many different ways can. 486 01:14:10.829 --> 01:14:14.939 You know, could you say marks the ballot or whatever while you could pick. 487 01:14:16.619 --> 01:14:21.840 You know, any number from Cape candidates on the ballot, you could. 488 01:14:21.840 --> 01:14:26.399 Pick any number from 0T to K of the candidates and. 489 01:14:28.289 --> 01:14:37.050 End of the candidates, and if you pick pay the and candidates, there's and choose K ways, you could do that. So it's the. 490 01:14:37.050 --> 01:14:41.220 Event choose K from caving 0T up to and. 491 01:14:42.569 --> 01:14:46.739 Which will net out to to to the end actually. So. 492 01:14:46.739 --> 01:14:53.880 So, there's an easier way. I could look at each candidate on the ballot and say, do I do not do I not pick that candidate? 493 01:14:53.880 --> 01:14:59.579 And that's to the end. So, preferential voting is a nice method. 494 01:14:59.579 --> 01:15:05.159 So, approval voting was a scheme to prevent. 495 01:15:05.159 --> 01:15:15.930 You know, the, you might say the establishment candidates, some splitting the vote evenly. So somebody who's actually not as popular getting in approval. Voting is another way. 496 01:15:15.930 --> 01:15:21.510 To solve that, if you in fact think that that's a problem that should be solved that gets out of this course. Now. 497 01:15:21.510 --> 01:15:25.829 So, preferential voting, which has a couple of different names. 498 01:15:25.829 --> 01:15:29.340 You're right rank order voting. You rank the candidates. 499 01:15:29.340 --> 01:15:32.909 So, how many ways can you can you mark the ballot there? 500 01:15:33.960 --> 01:15:37.619 Now, that gets harder because. 501 01:15:39.869 --> 01:15:45.569 You may not vote for everyone, so, and you have to pick it. So. 502 01:15:45.569 --> 01:15:50.970 Let's say, I try a little of that down. Maybe. 503 01:16:05.850 --> 01:16:15.149 Approval voting and candidates. 504 01:16:18.149 --> 01:16:25.590 Um. 505 01:16:25.590 --> 01:16:31.229 Because for each candidate, you can mark or not, you can vote for or not vote for that candle. 506 01:16:33.000 --> 01:16:41.100 Was the preference it's called rank? It's not other names also. 507 01:16:42.420 --> 01:16:47.609 Well, and candidates. 508 01:16:47.609 --> 01:16:48.000 Or, 509 01:16:47.994 --> 01:16:48.835 to the next page 510 01:17:03.863 --> 01:17:05.215 to vote for. 511 01:17:06.720 --> 01:17:12.569 Okay, well so and choose K ways you could put K. 512 01:17:15.239 --> 01:17:22.020 And actually, then you rank and the order K factorial basically your order matters. 513 01:17:25.829 --> 01:17:33.420 So a number of ways would be and factorial over and minus K factorial. And then you sum for K basically. 514 01:17:33.420 --> 01:17:42.000 And use some over K. so in total number of ways, you could mark, the ballot would be some of all the. 515 01:17:42.000 --> 01:17:51.000 Equals 0 2. N. okay. 516 01:17:51.000 --> 01:17:56.520 And that, I think has a simple answer, but I'm too tired to figure it out. Now. 517 01:17:57.569 --> 01:18:00.689 Probably, it's going to simplify, so. 518 01:18:06.659 --> 01:18:10.560 None of us, I take it back. 519 01:18:13.560 --> 01:18:17.100 But 1 way to simplify note of that equals. 520 01:18:17.100 --> 01:18:20.489 It equals the sum of all a cake was 0, 2 and. 521 01:18:20.489 --> 01:18:23.609 In factorial over K factorial. 522 01:18:25.260 --> 01:18:32.909 Equals yeah. 523 01:18:34.170 --> 01:18:40.140 So that they're equal sat there, I'll let you think about that, or you can ask questions and so on. 524 01:18:50.729 --> 01:18:55.260 Exactly. 1 is bad. 525 01:18:55.260 --> 01:18:59.220 Well, what I did is I did it in separate cases. 526 01:18:59.220 --> 01:19:03.899 Saying, well, if 1 is bad, maybe it's the 1st, 1. 527 01:19:03.899 --> 01:19:12.060 Maybe it's the 2nd, 1 maybe 3rd 1 maybe it's the 4th 1 maybe it's the 5th 1 and then in each of these 5 cases separately. 528 01:19:13.170 --> 01:19:17.699 Does that make sense, Andrew? So. 529 01:19:19.920 --> 01:19:23.609 If I go back to. 530 01:19:23.609 --> 01:19:34.470 here so exactly one is bad well perhaps a bad which is the first one or the second third fourth and fifth not it's a bad widget is the first one . 531 01:19:34.470 --> 01:19:38.279 There's 10 ways that could be bad to the next 4. good. 532 01:19:38.279 --> 01:19:45.659 90 times, times, 89 or maybe the bad widget is the 2nd 1. well, it turns out the formula is the same. 533 01:19:45.659 --> 01:19:54.329 The 1st word that I picked has got to be good 90 ways. 2nd widget gotta be bad. 10 way started, which it got to be good. Does 89 good widgets left. 534 01:19:54.329 --> 01:19:58.380 89, and so on, if we look at the case. 535 01:19:58.380 --> 01:20:04.710 Or the 3rd, which is the only bad widget it's going to be 90 times, 89 times 10. 536 01:20:04.710 --> 01:20:10.710 Times, 88 times, 87 not by the way is 87 there. 537 01:20:11.729 --> 01:20:15.420 That makes sense, I'll let you think about that. 538 01:20:23.939 --> 01:20:28.350 More a sense that okay, but not enough sense. Okay. 539 01:20:28.350 --> 01:20:31.380 Well, think about that can ask questions. 540 01:20:31.380 --> 01:20:35.609 Later okay reason I both time to stop. 541 01:20:35.609 --> 01:20:39.180 We don't we don't want to run late, so. 542 01:20:39.180 --> 01:20:44.039 So, we did up to here and I'll do more examples to try and. 543 01:20:44.039 --> 01:20:55.020 Help people understand that, and also you can watch Brad key. You can read the textbook and to be Tweet and I've got the textbook page numbers keyed in. 544 01:20:55.020 --> 01:21:07.560 And between all of that, we'll start figuring it out. I like to spend a little time on this basic stuff here because if this is confusing. 545 01:21:07.560 --> 01:21:12.750 You're going to be dead later on so I, I'd like to get the foundations solid. 546 01:21:12.750 --> 01:21:20.850 Story about foundations, so, Brooklyn Bridge, father and son team. A designers. The son was an graduate. 547 01:21:20.850 --> 01:21:25.739 And rich for 15 years to build. 548 01:21:25.739 --> 01:21:34.920 The 1st, 2 years that nothing visible was happening. They said they were spending a lot of money. You look over the East River ain't no bridge. 549 01:21:34.920 --> 01:21:41.880 And That'll bad press. Well, what were the roadblocks doing for 2 years building the foundations. 550 01:21:41.880 --> 01:21:47.100 Underwater cations, insulin, compressed air people getting bends and. 551 01:21:47.100 --> 01:21:55.859 That's by the way it's what down there a lot of it and so they spent 2 years on the foundations, but they did something right? Which is still there. 552 01:21:55.859 --> 01:22:00.810 All the rolling these bridges none of them ever collapsed. 553 01:22:00.810 --> 01:22:05.130 For his competitors can't say the same thing. 554 01:22:05.130 --> 01:22:09.270 So, I like to get foundations down. 555 01:22:09.270 --> 01:22:15.569 I'll hang around this question, so we pull up the chat window again where be the chat window. 556 01:22:16.979 --> 01:22:22.590 Ending ends now. Okay. 557 01:22:30.989 --> 01:22:36.869 Thank you. Yeah, well, I have Webex on my phone. 558 01:22:38.609 --> 01:22:46.050 And then point the phone that's crazy enough that I might actually do that. 559 01:22:46.050 --> 01:22:50.130 It's possible the phones Webex version will work better. 560 01:22:50.130 --> 01:22:55.829 Thank you that may actually be more reliable crazy, but reliable. 561 01:22:55.829 --> 01:22:59.819 Send me email me to remind me that's worth a point. 562 01:22:59.819 --> 01:23:03.390 Have a good weekend. See, you. 563 01:23:03.390 --> 01:23:04.109 Monday, 564 01:23:04.135 --> 01:23:50.875 Eva.