A pharmaceutical company manufacturing pregnancy test kits wants to determine the probability of a woman actually being pregnant when the test results indicate that she is not pregnant.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 that she is not pregnant.What is the probability that she is pregnant?

Question

Quizplus · Accepted Answer

P(Pregnant|Negative) = P(Negative|Pregnant) * P(Pregnant) / P(Negative)P(Negative|Pregnant) = 1/200P(Pregnant) = 0.1P(Negative) = P(Negative|Pregnant) * P(Pregnant) + P(Negative|Not Pregnant) * P(Not Pregnant)P(Negative|Not Pregnant) = 1/100P(Not Pregnant) = 1 - P(Pregnant) = 0.9P(Negative) = 1/200 * 0.1 + 1/100 * 0.9 = 0.0095P(Pregnant|Negative) = 1/200 * 0.1 / 0.0095 = 0.00056

A Pharmaceutical Company Manufacturing Pregnancy Test Kits Wants to Determine