00:01
So we want to start out by drawing our tree diagram of our situation.
00:06
And so we know that we either have the antigen and i'm going to say yes or we don't have the antigen.
00:14
And it tells us that we're to assume that 1 % of the population has the antigen, which means that 99 % don't have the antigen.
00:25
And then we have a table that helps us see whether someone test positive or does.
00:31
Doesn't test positive.
00:35
And so from our table, we're told that of those people that have the antigen, that the positive rate is .9985.
00:47
And the negative rate, which they didn't really have to tell us, these two have to add up to one, but they give us that little tidbit is .0015.
00:57
And if the antigen is not present, then the positive rate is .006.
01:06
And again, since i gave us this, these two in this branch have to add up to one, but they told us that this has to be .994.
01:15
So now we want to look at this and determine what's the probability that someone tests positive.
01:24
And we know we have two ways to test positive.
01:27
You can either have the antigen and test positive, or you can not have the antigen.
01:39
Test positive.
01:42
And so we will multiply 0 .01 times .9985.
01:52
And that product of these two probabilities will give us this intersection.
01:57
That's the likelihood that you randomly choose a person and the person has the antibody and they test positive.
02:04
Or, or was a mean add, we have someone who really is negative.
02:13
However, they test positive.
02:20
And when we do that calculation and add those together, we end up getting .01592...