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Chapter 5: Q .78. (page 336)

. At the gym Suppose that 10% of adults belong to health clubs, and 40% of these health club members go to the club at least twice a week. Find the probability that a randomly selected adult belongs to a health club and goes there at least twice a week.

Short Answer

Expert verified

Probability for a randomly selected adult belongs to a health club and visit club at least twice a week is0.04.

Step by step solution

01

Step 1:Given information

Adults who subscribe to health clubs make about 10% of the population.

At least twice a week, 40% of these fitness club members visit the facility.

02

Step 2:Calculation

According to general multiplication rule,

P(AandB)=P(A∩B)=P(A)×P(B∣A)=P(B)×P(A∣B)

Let

H: adults belong to health clubs

W: health club members go to the club at least twice a week

Now,

The corresponding probabilities:

Probability for the adults belong to health clubs,

P(H)=0.10

Probability for the health club members go to the club at least twice a week,

P(W∣H)=0.40

Use the following multiplication rule:

P(HandW)=P(H∩W)=P(H)×P(W∣H)

=0.10×0.40

=0.04

Thus,

Probability for a randomly selected adult belongs to a health club and visit club at least twice a week is0.04.

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