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

Answer:

0.5885

Step-by-step 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:

$P(P|+) = \frac{0.95*0.07}{0.113}\\P(P|+) = 0.5885$

The probability is 0.5885