00:01
It's given in this question that the prevalence of a disease in a population is 1%.
00:06
So that means for any randomly selected person from this population, the probability that they have this disease is 0 .01.
00:15
It's also given that the probability of a true positive for a test for this disease is 95%.
00:22
So that means that the probability of testing positive, given that you have the disease, is 0 .95.
00:29
And the probability of a true negative is also 95%.
00:36
We are asked, if a person tests positive, what is the probability that they actually have the disease? so this is the probability of d, given positive.
00:52
To solve this conditional probability, we can make use of bayes ' theorem.
01:00
Bayes ' theorem says that the probability of an event b given a is equal to the probability of a given b, times the probability of b, divided by the probability of a.
01:16
So for our scenario, we can equate this 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.
01:30
Now we have the probability of having the disease, that's 0 .01.
01:36
We have the probability of testing positive, given that you have the disease, 0 .95...