Question

. 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

Probability for a randomly selected adult belongs to a health club and visit club at least twice a week is$0.04.$

Step-by-step solution

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.

Step 2:Calculation

According to general multiplication rule,

$P(\mathrm{A}\text{and}\mathrm{B})=P(\mathrm{A}\cap \mathrm{B})=P(\mathrm{A})\times P(\mathrm{B}\mid \mathrm{A})=P(\mathrm{B})\times P(\mathrm{A}\mid \mathrm{B})$

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,

$P\left(H\right)=0.10$

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

$P(\mathrm{W}\mid \mathrm{H})=0.40$

Use the following multiplication rule:

$P\left(\mathrm{H}\text{and}\mathrm{W}\right)=P(\mathrm{H}\cap \mathrm{W})=P\left(\mathrm{H}\right)\times P(\mathrm{W}\mid \mathrm{H})$

$=0.10\times 0.40$

$=0.04$

Thus,

Probability for a randomly selected adult belongs to a health club and visit club at least twice a week is$0.04.$