A pharmaceutical company manufacturing pregnancy test kits wants to determine the probability of a woman not being pregnant when the test results indicate pregnancy.It is estimated that the probability of pregnancy among potential users of the kit is 10%.According to the company laboratory test results,1 out of 100 non-pregnant women tested pregnant (false positive).On the other hand,1 out of 200 pregnant women tested non-pregnant (false negative).A woman has just used the pregnancy test kit manufactured by the company and the results showed pregnancy.What is the probability that she is not pregnant?

Question

Quizplus · Accepted Answer

Let's use Bayes' theorem to solve this problem.
Let P(P) be the probability of a woman being pregnant (prior probability) = 0.1
Let P(N) be the probability of a woman not being pregnant = 0.9
Let P(Pos|P) be the probability of a positive test result given that the woman is pregnant = 0.995 (since 1 out of 200 pregnant women tested negative)
Let P(Neg|N) be the probability of a negative test result given that the woman is not pregnant = 0.99 (since 1 out of 100 non-pregnant women tested positive)
Using the formula:
P(P|Pos) = P(Pos|P) * P(P) / [P(Pos|P) * P(P) + P(Pos|N) * P(N)]
= 0.995 * 0.1 / [0.995 * 0.1 + 0.01 * 0.9]
= 0.917
Therefore, the probability that the woman is not pregnant given a positive test result is 0.083.

A Pharmaceutical Company Manufacturing Pregnancy Test Kits Wants to Determine