math homework help

Question

Suppose that 4% of all adults suffer from diabetes and that 31% of all adults are obese. Suppose also that 2% of all adults both are obese and suffer from diabetes.(a) Find the probability that a randomly chosen adult is obese, given that he or she suffers from diabetes. Round your answer to 2

 decimal places.

(b) Find the probability that a randomly chosen adult who is obese also suffers from diabetes. Round your answer to 2 decimal places.

Answer 1

For this question, you will need to use the conditional probability formula.

The probability of B given A is equal to the probability of A and B divided by the probability of A.

In part A, you are looking for the probability that a person is obese given that he has diabetes. In this case, obesity is your B and being diabetic is your A. P(A) is the probability of being diabetic and P(B) is the probability of being obese. The probabilities are given by the percentages, for example, 4% of adults are diabetic, so P(A) = 0.04. You are also given the probability of being both obese and diabetic, which gives you P(A and B). Now you have enough information to put into the equation and solve.

In part B, you are given that the person is obese and want to find the probability that he also has diabetes. You can use the same equation to find this part. The only difference is that being diabetic is your B and obesity is your A.