Question

A group of volunteers for a clinical trial consists of 81 women and 77 men. 18 of the women and 19 of the men have high blood pressure. If one of the volunteers is selected at random find the probability that the person has high blood pressure given that it is a woman.

Answer 1

0.22

Explanation:

Let the events be:

A: the person is a woman

B: the person has high blood pressure

We want to find P(B/A), that is, the probability that a person has high blood pressure given that is a woman. We can use the following theorem:

P(B/A) = P(A∩B)/P(A)

P(A∩B) is the probability that a person is a woman and has high blood pressure. Given that there are 18 women with high blood pressure and 158 persons in total (81 + 77),

P(A∩B) = 18/158

P(A) is the probability that a person is a woman. Given there are 81 women and 158 persons in total,

P(A) = 81/158

P(B/A) = P(A∩B)/P(A)

P(B/A) = (18/158)/(81/158) = 0.22