WEBVTT 1 00:00:01.290 --> 00:00:02.123 Hello, students. 2 00:00:02.123 --> 00:00:04.263 Now we are going to problem six B. 3 00:00:05.220 --> 00:00:07.620 So I'm going to read the problem again. 4 00:00:07.620 --> 00:00:09.750 A study is conducted to assess the impact 5 00:00:09.750 --> 00:00:12.840 of caffeine consumption, smoking, alcohol consumption, 6 00:00:12.840 --> 00:00:16.380 and physical activity on cardiovascular disease. 7 00:00:16.380 --> 00:00:20.850 Suppose that 40% of participants consume caffeine and smoke. 8 00:00:20.850 --> 00:00:25.230 If eight participants are evaluated, what is the probability 9 00:00:25.230 --> 00:00:28.893 that more than six consume caffeine and smoke? 10 00:00:31.470 --> 00:00:34.800 So here, more than six means seven and eight 11 00:00:34.800 --> 00:00:37.890 because we have a total of eight participants. 12 00:00:37.890 --> 00:00:39.753 So let's start writing that. 13 00:00:57.390 --> 00:01:00.303 Again we are going to use the binomial distribution. 14 00:01:09.960 --> 00:01:13.380 As I said before, I like to write the formula again, 15 00:01:13.380 --> 00:01:15.153 so it is here, 16 00:01:16.410 --> 00:01:21.410 X successes equal to... 17 00:01:50.100 --> 00:01:53.250 So now basically we have to do this calculation twice, 18 00:01:53.250 --> 00:01:56.613 once for seven and once for eight. 19 00:02:39.360 --> 00:02:40.810 So once we do this, 20 00:02:43.530 --> 00:02:46.773 again, I would like to write this a little bit. 21 00:02:49.530 --> 00:02:53.043 So eight factorial means eight times seven factorial. 22 00:02:54.090 --> 00:02:55.530 In the bottom we have now, 23 00:02:55.530 --> 00:02:58.983 it's seven factorial in the denominator, 24 00:03:00.480 --> 00:03:02.250 and eight minus seven is one, 25 00:03:02.250 --> 00:03:04.113 and then it is one factorial. 26 00:03:07.830 --> 00:03:12.830 So this one would be 0.4 to the power seven. 27 00:03:12.930 --> 00:03:14.910 Again, as you use your calculator, 28 00:03:14.910 --> 00:03:16.247 you will get .00164. 29 00:03:22.318 --> 00:03:23.651 This one will be 30 00:03:27.165 --> 00:03:29.165 0.6 to the power of one. 31 00:03:45.360 --> 00:03:48.677 So once we do this calculation, we get 0.0079. 32 00:03:54.931 --> 00:03:57.270 Okay, so what I'm going to do is I'm going 33 00:03:57.270 --> 00:03:59.310 to put this one actually up there 34 00:03:59.310 --> 00:04:02.990 so I have enough space to do the other calculation 35 00:04:07.620 --> 00:04:08.970 here. 36 00:04:08.970 --> 00:04:13.970 So for eight, we have to kind of repeat the process 37 00:04:15.810 --> 00:04:17.670 except the numbers, of course, will change. 38 00:04:17.670 --> 00:04:20.190 It's going to be eight factorial up here. 39 00:04:20.190 --> 00:04:23.160 It's going to be eight factorial down here, 40 00:04:23.160 --> 00:04:25.773 eight minus eight factorial. 41 00:04:28.110 --> 00:04:33.000 Here it's going to be 0.4 to the power eight. 42 00:04:33.000 --> 00:04:37.473 And again, here it's going to be one minus 0.4, 43 00:04:39.655 --> 00:04:41.163 8 minus eight. 44 00:04:45.030 --> 00:04:48.240 So once we do this algebraically, 45 00:04:48.240 --> 00:04:50.470 what we get as the result here is 46 00:04:53.584 --> 00:04:55.503 0.0007. 47 00:04:57.660 --> 00:05:01.653 So for our final answer, what we have to do is add them. 48 00:05:36.030 --> 00:05:38.880 So going back to the question of this problem, 49 00:05:38.880 --> 00:05:41.730 it says, "What is the probability that more 50 00:05:41.730 --> 00:05:44.790 than six consume caffeine and smoke?" 51 00:05:44.790 --> 00:05:49.790 So that probability is going to be 0.0086, 52 00:05:49.860 --> 00:05:52.530 and, of course, you can multiply it by 100 53 00:05:52.530 --> 00:05:54.813 and get it into the percentage.