0:00
We're given quite a bit of information.
00:01
And the first information, in part a, we want to find, look at this tree.
00:06
We want to look at people who are infected with hiv and those who are not.
00:12
And then we know for testing positive that this is 99 % chance.
00:18
This is a 1 % chance.
00:20
And if you do not have hiv, you have a 99 % chance of testing negative and a 1 % chance of testing positive.
00:28
Now, what is the likelihood of each of these? well, we know that there are 550 ,000 people who have hiv out of a total of 250 million people in the u .s.
00:49
Population.
00:50
So when we divide this, we find out that this is 0 .0022, which means that the likelihood of not being infected is 0 .997 .8.
01:00
And so we can answer our first question.
01:03
Our first question we want to find, given that someone test positive, what is the likelihood that someone actually has hiv? so for this scenario, we want to find what the likelihood of positive is to begin with.
01:17
And we have two ways to be positive.
01:20
This track, where we go 0 .0022 times .99, or we can have this track, which is a false positive.
01:30
And that's .9978 times .01.
01:34
Let's get that total, first of all, .0022 times .99 plus .9978 times .01.
01:45
And that gives us a probability of testing positive of .012156.
01:54
And i'm actually going to store that value of x is x in my calculator.
01:57
And so to find this probability, we have to find the probability of hiv and test positive divided by and that's and and divide that by the probability of positive so the numerator is going to be the 0 .022 times 0 .99 that's the likelihood of having hiv and testing positive and the denominator is at 0 .012156 so 0 .0022 .9 .0 .022 times 0 .99 divided by that value.
02:34
And this comes out to be 0 .179 and 17.
02:40
And then you can round that to whatever dazzle of place you need.
02:43
Now we have a second question.
02:46
And we want to find the probability on this one...