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 third as likely to develop diabetes compared with men who were sedentary. assume that one in 10 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.)

0.0357

Step-by-step explanation:

We have the following important data:

One in 10 middle-aged men is very active, and the rest are classified as sedentary.Men who were very active (burning about 3,500 calories daily) were a third as likely to develop diabetes.From point 1) we can say that the relation between very active and sedentary men is 1 to 9. That is, for each very active man there are 9 sedentary men.From point two we can say that, if we had the same number of sedentary and very active men, then there would be 3 times more sedentary men with diabetes than very active men with diabetes.

But we do not have the same number of sedentary and very active men. There are 9 times more sedentary than very active. Therefore, there would be 9*3=27 times more sedentary men with diabetes than very active men with diabetes.

In conclusion, the probability that a middle-aged man with diabetes is very active is