00:01
In this question, we are given the following probabilities and conditional probabilities.
00:07
If someone has the disease, we'll call that event d.
00:10
The probability of them testing positive in the test, call that plus, is 0 .95.
00:18
If someone does not have the disease, we'll call that d prime.
00:23
The probability of them testing negative then is 0 .90.
00:26
And we are also told that .999 of the population do not have the disease.
00:36
So that's the probability of d prime.
00:40
We are asked for the probability that somebody has the disease if the test is positive.
00:47
So that is what is the probability of d given positive? the way we can solve this is to use bases theorem, which basically says that the probability of b given a is equal to the probability of a given b times the probability of b divided by the probability of a.
01:25
So for our scenario, the probability of having the disease, given that you tested positive, is equal to the probability of testing positive, given that you have the disease, times the probability of having the disease, divided by the probability of testing positive, the overall probability of testing positive.
01:48
Now if the probability of testing negative, given that you do not have the disease, is 0 .9.
01:58
This means that the probability of testing positive, given that you don't have the disease, must be 0 .1.
02:08
If you don't have the disease, you have to test either positive or negative.
02:12
So these two probabilities have to add up to 1...