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 percent.According to the company laboratory test results,1 out of 100 nonpregnant women tested pregnant (false positive).On the other hand,1 out of 200 pregnant women tested nonpregnant (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

Using Bayes' theorem, the probability of not being pregnant given a positive test result is calculated as follows: P(Not Pregnant | Positive) = (P(Positive | Not Pregnant) * P(Not Pregnant)) / P(Positive). Here, P(Positive | Not Pregnant) = 0.01, P(Not Pregnant) = 0.9, and P(Positive) = (0.01 * 0.9) + (0.995 * 0.1) = 0.1085. Thus, P(Not Pregnant | Positive) = (0.01 * 0.9) / 0.1085 ≈ 0.083 or 8.3%.

A Pharmaceutical Company Manufacturing Pregnancy Test Kits Wants to Determine