(1 point) Recall that Bayes' Theorem states that P(Bi|A)=P(Bi)P(A|Bi)P(B1)P(A|B1)++P(Bn)P(A|Bn)P(Bi|A)=P(Bi)P(A|Bi)P(B1)P(A|B1)++P(Bn)P(A|Bn).

In this problem we will illustrate Bayes' Theorem.

A new medical test has been designed to detect the presence of a genetic disease. Among those who have the disease, the probability that the disease will be detected by the new test (true positive) is 0.9 and the probability that the disease will not be detected (false negative) is 0.1.

The probability that the test will not detect the disease in those who do not have it (true negative) is 0.95 and the probability that the test will erroneously detect the presence of the disease in those who do not actually have it (false positive) is 0.05.

Suppose 1000 people take the test and assume that 3% of the population who take this test have the disease.

Fill in the following table (It is okay to have fractional numbers as answers).

	Test +	Test -	Totals
Have the Disease
Do Not Have the Disease
Totals

If the is test administered to an individual is positive, what is the probability that the person has the disease? Note your answer is the same for any population size -- not just 1000.

P(Have Disease | +) =

Is this answer significantly different from what you initially thought given the true positive probability? This is because of the relatively low percentage of the population that has the disease. Sometimes your intuition can't be trusted.