According to Health magazine (July/August 1992), the probability of pregnancy in

Question

According to Health magazine (July/August 1992), the probability of pregnancy in the first year is 0.12 for typical users of condoms (which include couples who occasionally forget to use the method or don't use it correctly). However, the probability of pregnancy is only 0.02 for perfect users (those who use the condom correctly each time). 1. List all the probabilities given in this problem, expressed in terms of events that you define. Suppose 20% of couples using condoms are perfect users, and the remaining 80% are typical users. If a couple using a condom for birth control is selected at random, what is the probability the woman will become pregnant in the first year of use? If the woman becomes pregnant in the first year of use, what is the probability she was a perfect user? a) b) c)

Explanation / Answer

Let T shows the event that the couple is a typical user and P shows the event that couple is a perfect user.

a)

Let S shows the event that woman become pregnant in the first year of use. So from the given infromation we have

P(S | T) = 0.12 , P(S | P) = 0.02

b)

Here we have

P(P) = 0.20, P(T) = 0.80

By the law of total probability, the probability that woman become pregnant in the first year is

P(S) = P(S|T)P(T) + P(S|P) P(P) = 0.12 * 0.80 + 0.02 * 0.20 = 0.096 + 0.004 = 0.100

c)

The requried probability is

P(P|S) = [P(S|P) P(P)] / P(S) = 0.004 / 0.100 = 0.04

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