Question

A test for a disease gives a correct positive result with a probability of 0.90 when the disease is present but gives an incorrect positive result with a probability of 0.10 when the disease is not present. If 10% of the population has the disease, and Rohini tests positive, then what is the probability that Rohini has the disease?

Answer 1

To calculate the probability that Rohini has the disease given that she tested positive, we can use Bayes' theorem. Given the probabilities of the disease and test results, we can substitute these values into the formula to find the probability.

Step-by-step explanation:

To calculate the probability that Rohini has the disease given that she tested positive, we can use Bayes' theorem. Let's define D as the event that someone has the disease, and P as the event that someone tests positive. Now we can calculate the probability using the formula:

P(D|P) = (P(D) * P(P|D)) / P(P)

Given that 10% of the population has the disease (P(D) = 0.1), and the test gives a correct positive result with a probability of 0.90 when the disease is present (P(P|D) = 0.9), we need to find P(P).

Since the test gives an incorrect positive result with a probability of 0.10 when the disease is not present, we can calculate P(P) using the formula:

P(P) = P(P|D) * P(D) + P(P|~D) * P(~D)

Given that P(P|~D) = 0.10 and P(~D) = 0.9, we can now substitute the values into the formula to find P(P).

Once we have the value of P(P), we can substitute all the values into the first formula to calculate the probability that Rohini has the disease given that she tested positive.