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 in 15 middle-aged men is 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

Suppose men who very active were a fifth as likely to develop diabetes compared with men who were sedentary Let the probability of active men developing diabetes be A. Then, the probability of sedentary men developing diabetes is 54 Consider - th of all middle-aged men are very active, and the rest are classified as sedentary Probability active men develope diabetes is, Pactive and developes diabetes) = Axpopulation of active men = AX75 Let the total population be 1. Then, ratio of sedentary men = 1-ratio of active men =1-15 Probability sedentary men develope diabetes is, P(sedentary and developes di abetes ) = 5 Ax population of sedentary men =54x14 15 70A 15 -------------------------------------- - By the Baye's theorem, Probability a middle-aged man with diabetes is very active P[active and developes di abetes) P(active and developes diabetes) +P(sedentary and developes diabetes) = 71 15 = 71 0.0141