WEBVTT 1 00:00:01.590 --> 00:00:02.670 Hello, students. 2 00:00:02.670 --> 00:00:07.530 We are now going to go over problem 6A. 3 00:00:07.530 --> 00:00:10.890 This is the last problem we are covering from chapter five. 4 00:00:10.890 --> 00:00:14.310 I know this has been a lot, but I really do want to go 5 00:00:14.310 --> 00:00:17.550 over these problems because this will help you 6 00:00:17.550 --> 00:00:19.380 not only do the homework problems, 7 00:00:19.380 --> 00:00:22.140 but also to do well in the test. 8 00:00:22.140 --> 00:00:25.830 So problem six again states a study is conducted 9 00:00:25.830 --> 00:00:28.770 to assess the impact of caffeine consumption, 10 00:00:28.770 --> 00:00:30.660 smoking, alcohol consumption 11 00:00:30.660 --> 00:00:33.900 and physical activity on cardiovascular disease. 12 00:00:33.900 --> 00:00:38.850 Suppose that 40% of participants consume caffeine and smoke. 13 00:00:38.850 --> 00:00:41.430 If eight participants are evaluated, 14 00:00:41.430 --> 00:00:45.180 what is the probability that exactly four 15 00:00:45.180 --> 00:00:48.389 do not consume caffeine or smoke? 16 00:00:48.389 --> 00:00:51.690 So from reading the problem, I think you kind of understand 17 00:00:51.690 --> 00:00:54.600 that here we are kind of doing the reverse 18 00:00:54.600 --> 00:00:58.960 of what we did in part A, but it is a little different 19 00:00:59.910 --> 00:01:04.910 but we still have four, we just have, 20 00:01:04.950 --> 00:01:06.660 but now we are looking for four 21 00:01:06.660 --> 00:01:09.333 that do not consume caffeine or smoke. 22 00:01:11.040 --> 00:01:14.070 However, we have to use the same binomial distribution 23 00:01:14.070 --> 00:01:19.070 and therefore, I start writing the formula again. 24 00:02:06.240 --> 00:02:08.100 However, as you can see here 25 00:02:08.100 --> 00:02:09.900 that the probability will change 26 00:02:09.900 --> 00:02:13.380 because now there is a 40% 27 00:02:15.180 --> 00:02:16.683 of the participants, 28 00:02:18.316 --> 00:02:19.560 (instructor clearing throat) excuse me, 29 00:02:19.560 --> 00:02:21.300 who consume caffeine or smoke. 30 00:02:21.300 --> 00:02:24.210 So 60% does not. 31 00:02:24.210 --> 00:02:25.800 So because of this, 32 00:02:25.800 --> 00:02:29.130 we are going to be doing this a little bit differently. 33 00:02:29.130 --> 00:02:32.490 Well, the probability here basically will be changing. 34 00:02:32.490 --> 00:02:37.490 So here we have still x equal to four, 35 00:02:38.430 --> 00:02:41.400 here the n is still eight. 36 00:02:41.400 --> 00:02:42.900 That is not going to change. 37 00:02:42.900 --> 00:02:46.170 So it's eight factorial, again, four factorial 38 00:02:46.170 --> 00:02:48.423 eight minus four factorial. 39 00:02:51.720 --> 00:02:55.863 However, this p right now will be 0.6 to the power four. 40 00:02:56.820 --> 00:03:01.590 And this will be be one minus 0.6 41 00:03:01.590 --> 00:03:06.590 and that will be to the power eight minus four. 42 00:03:06.630 --> 00:03:10.200 So here, if you recall, we already did this part 43 00:03:10.200 --> 00:03:14.910 of the calculation in part A, so I'm not going to repeat it. 44 00:03:14.910 --> 00:03:19.530 So what I'm going to do is basically write this down 45 00:03:19.530 --> 00:03:23.457 as two times seven times five 46 00:03:28.050 --> 00:03:32.623 and then 0.6 to the power four will be again 0.1296 47 00:03:37.680 --> 00:03:40.950 and this one will be 0.0256. 48 00:03:44.310 --> 00:03:47.760 So when we do this multiplication all the way, 49 00:03:47.760 --> 00:03:52.760 we get 0.2322, and basically that is 23.22%. 50 00:03:58.440 --> 00:04:02.790 So basically, we have ended up with almost the same result. 51 00:04:02.790 --> 00:04:06.240 So going back again to our problem statement, 52 00:04:06.240 --> 00:04:08.850 if eight participants are evaluated, 53 00:04:08.850 --> 00:04:10.110 what is the probability? 54 00:04:10.110 --> 00:04:13.350 So the probability is 23.22, 55 00:04:13.350 --> 00:04:18.350 exactly four that do not consume caffeine or smoke. 56 00:04:21.990 --> 00:04:25.170 So that's basically the conclusion. 57 00:04:25.170 --> 00:04:27.000 And I will write this one down 58 00:04:27.000 --> 00:04:28.890 because we do have some space here. 59 00:04:28.890 --> 00:04:33.890 So the probability is 23.22% 60 00:04:36.480 --> 00:04:37.653 probability, 61 00:04:42.390 --> 00:04:44.520 or if you really want to be cor, 62 00:04:44.520 --> 00:04:48.753 we can say 0.2322. 63 00:04:51.900 --> 00:04:53.110 Probability 64 00:04:58.620 --> 00:05:00.820 that exactly 65 00:05:07.170 --> 00:05:08.003 four 66 00:05:10.050 --> 00:05:10.883 do not 67 00:05:13.950 --> 00:05:15.873 consume caffeine or smoke. 68 00:05:27.956 --> 00:05:29.610 Okay. All right. 69 00:05:29.610 --> 00:05:32.700 So thank you again very much for your patience 70 00:05:32.700 --> 00:05:36.030 and going with me through all these problems. 71 00:05:36.030 --> 00:05:39.030 Chapter five, we have covered quite a few problems. 72 00:05:39.030 --> 00:05:41.670 Again, it's very important you go through these problems, 73 00:05:41.670 --> 00:05:44.760 not once, but at least a couple of times. 74 00:05:44.760 --> 00:05:46.560 It'll really, really help you. 75 00:05:46.560 --> 00:05:48.600 I really enjoyed solving these problems 76 00:05:48.600 --> 00:05:52.200 and hopefully, you have enjoyed learning this too. 77 00:05:52.200 --> 00:05:54.510 So again, please feel free to reach out 78 00:05:54.510 --> 00:05:55.830 if you have any questions. 79 00:05:55.830 --> 00:05:56.733 I'm here to help.