Question

According to a study in a medical journal, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that men who were very active (burning about 3,500 calories daily) were a fifth as likely to develop diabetes compared with men who were sedentary. Assume that one-third of all middle-aged men are very active, and the rest are classified as sedentary. What is the probability that a middle-aged man with diabetes is very active? (Round your answer to four decimal places.)

Answer 1

Let us consider the event

A - the event that a middle-aged man is active.

B - the event that a middle-aged man has diabetes.

It is given that one-third of all middle-aged men are very active, therefore P(A) = 1/3

And, 202 of a sample of 5,990 middle-aged men had developed diabetes, therefore P(B) = 202/5990

It is also found that men who were very active were a fifth as likely to develop diabetes,

The probability that a middle-aged man with diabetes is very active is