Question

Use the tree diagram technique that can be found in Lecture 12 to solve this problem. Suppose that 50% of all people who take a pregnancy test are, in fact, pregnant. A certain pregnancy test is known to identify 95% of pregnancies with a positive test result. However, 2% of people who are not pregnant will have a positive test result.

Find the following probabilities:

a. What is the probability that someone is pregnant and tests positive?

b. What is the overall probability of a positive test result?

c. If a woman has a positive test result, what is the probability that she is actually pregnant?

Answer 1

a) P(pregnant and test positive) = P(test positive | pregnant) * P(pregnant)

                                                   = 0.95 * 0.50 = 0.475

b) P(Positive test) = P(positive | pregnant) * P(pregnant) + P(positive | not pregnant) * P(not pregnant)

                             = 0.95 * 0.50 + 0.02 * (1 - 0.50)

                             = 0.485

c) P(pregnant | positive) = P(positive | pregnant) * P(pregnant)/P(positive)

                                      = (0.95 * 0.50)/0.485

                                      = 0.9794