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.)

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Mathematics

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1 June, 05:22

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.)

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Kaylee Pacheco · Answer 1

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

Step-by-step 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