Suppose that for all those individuals with positive first blood test results for the disease, a second blood test will be conducted. And the second blood test for Joe again shows up positive. Assume that the test results are independent given an individual's true disease status, what is the conditional probability that the disease is actually present in Joe given his two positive test results

0.25

Step-by-step explanation:

Every time the test is conducted, there is a chance that the result will either be false/true positive or false/true negative. Let's assign each outcome a probability of 0.25. If he tested positive, it could either be a false positive or true positive so 0.25 + 0.25 = 0.5

Then if he gets tested a second time, the result could again be a false positive or true positive so 0.25 + 0.25 = 0.5

Now we need to multiply the probabilities with each other 0.5 * 0.5 = 0.25