00:02
Okay, so in this problem, we have to first determine the random variable x and its distribution.
00:09
So let's write it right here.
00:11
So x, we know that it is binomial.
00:16
So whether you commit suicide or not commit suicide, it is kind of sad, but it is binomial with the number of trials is 1 ,000 because there are 1 ,000 people.
00:27
And the probability of success, in this case success means committing suicide.
00:34
So let's just leave it as p because it is unknown.
00:39
So let's calculate what p is first so that we can solve all other questions.
00:45
So to calculate the probability of suicide, so by the law of total probability, we can compute this probability by using the probability of suicide.
01:08
I'll just write sui for suicide.
01:11
Suicide given cold times probability of cold plus probability of suicide given not cold and c stands for not the town not being cold times probability of not being cold.
01:31
So this is by the law of total probability.
01:35
So when you do that, we get that it's, all of these numbers are given in the problem, right? so it is 0 .005 for the probability of suicide given the town being cold and the probability of being cold is 0 .2 plus 0 .002 for some town that is not cold and the probability of not being cold is 0 .8.
02:05
That is straight from 1 minus 0 .2 because the event of a town being cold and not being cold is a complement...