At any given time about 5.5% of women (age 15-45) are pregnant. A home pregnancy test is accurate 99% of the time if the woman taking the test is actually pregnant and 99.5% accurate if the woman is not pregnant. If the test yields a positive result, what is the posterior probability of the hypothesis that the woman is pregnant? a. 0.08 b. 0.995 c. 0.92 d. 0.99

The correct option is (c). 0.92

Step-by-step explanation:

Let X = a woman is pregnant and Y = a pregnancy test is positive.

Given:

According to the Bayes' theorem, the conditional probability of an event A given than another event B has already occurred is:

Use the above formula to compute the probability that a woman is pregnant given that the pregnancy test is accurate as follows:

Thus, the probability that a woman is pregnant given that the pregnancy test is accurate is 0.92.

The correct option is (c).

the answer will be