In a study of the relationship between health risk and incom

In a study of the relationship between health risk and income, a large group of people living in Massachusetts were asked a series of questions. Some of the results are shown in the following table.

Solution

(a) Probability that someone in the study is stressed(A say) is 1016/6549 = 0.1551

(b) Probability that the person is stressed (A say) given that someone in this study is from high income group (B say) is

P(A/B) = P(A and B) / P(B) = (216/6549) / (2115/6549) =216/2115 = 0.1021.

(c) Here, P(A/B) not equal to P(A)

Therefore, Stress(A) is not independent of having high income(B).

Note: 1. If P(A/B) = P(A) then events A and B are independent

2. if P(B/A) = P(B) then events A and B are indepdent.

3. if P(A and B) = P(A).P(B) then Events A and B are independent.