Question

Suppose that a pregnancy test kit, while tested on women, produces 95% true positive and 90% true negative. Suppose that 7% of women are pregnant. What is the probability that a randomly selected woman who is teted positive, is actually pregnant?

Answer 1

0.5885

Explanation:

The possible ways for a test to be positive are:

- Woman is pregnant & true positive

- Woman is not pregnant & false positive

The probability of a positive is:

`P(+) = 0.07*0.95+(1-0.07)*(1-0.95)\\P(+)=0.113`

Therefore, the probability that a woman is actually pregnant given that she tested positive is:

`P(P|+) = (0.95*0.07)/(0.113)\\P(P|+) = 0.5885`

The probability is 0.5885