A home pregnancy test is not always accurate Suppose the pro

A home pregnancy test is not always accurate. Suppose the probability is 0.015 that the test indicates that a woman is pregnant when she actually is not, and the probability is 0.025 that the test indicates that a woman is not pregnant when she really is. Assume that the probability that a woman who takes the test is actually pregnant is .7. What is the probability that a woman is pregnant if the test yields a not-pregnant result?

Solution

Let

P = pregnant
+ = positive
- = negative

Thus,

P(P|-) = P(P) P(-|P) / P(-)

As

P(-) = P(P) P(-|P) + P(P\') P(-|P\') = 0.7*0.025 + (1-0.7)*(1-0.015)

P(-) = 0.313

Thus,

P(P|-) = P(P) P(-|P) / P(-) = 0.7*0.025/0.313 = 0.055910543 [ANSWER]