Question

Suppose that 20% of adults belong to health clubs, and 51% of these health club members go to the club at least twice a week. What percent of all adults go to a health club at least twice a week? Write the information given in terms of probabilities and use the general multiplication rule. (Let H be the event that an adult belongs to a club, and T be the event that he/she goes at least twice a week. Use 3 decimal places.)

Answer 1

10.2% of adults will belong to health clubs and will go to the club at least twice a week

Explanation:

assuming that the event H=an adult belongs to a health club and the event T= he/she goes at least twice a week , then if both are independent of each other:

P(T∩H)= P(H)*P(T) ( probability of the union of independent events → multiplication rule )

replacing values

P(T∩H)= P(H)*P(T) = 0.20 * 0.51 =0.102

then 10.2% of adults will belong to health clubs and will go to the club at least twice a week