A test for a disease gives a correct positive result with a...

A test for a disease gives a correct positive result with a probability of 0.95 when the disease is present, but gives an incorrect positive result (false positive) with a probability of 0.15 when the disease is not present. If 5% of the population has the disease, and Jean tests positive to the test, what is the probability Jean really has the disease?

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Transcript

00:01 It is given that a test for a disease gives a correct positive result with probability 0 .95 when the disease is present.

00:12 So if we denote s as the event of being a sufferer and n s as the event of being non -suffer and p be the event of getting positive result.

00:36 Then we can denote this 0 .95 as probability of p given yes when it is given that the person is suffered the probability of getting positive result is equal to 0 .95 similarly we can denote p of p given n s as 0 .15 when the selected person is a non -sufferer, the probability of getting a positive result is equal to 0 .15.

01:15 Also, it is given that 5 percentage of population has the disease.

01:20 It means that out of 100 people, there are 5 people who have that particular disease.

01:27 So it can be denoted by p of s.

01:30 So, p of s is equal to 0 .05.

01:35 Now understand that we are as to find the probability of gene having the disease where it is given that his test result is positive.

01:54 So what we can say is we want the probability of yes given p.

02:03 When it is given that the test result is positive, we need to find the probability of gene actually being a sufferer.

02:10 So the required probability p of s given p is given by the formula.

02:17 P of s times p of p given s divided by p of p of p.

02:25 We know the value of p of s...