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. 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.

Short answer

The percentage of all adults go to health club is 4%

Step-by-step solution

Step 1. Given Information

$10\%$ of adults subscribe to a fitness club, with $40\%$ of these members going at least twice a week.

Step 2. Concept Used

Multiplication rule $P(A\cap B)=P(A\cap B)\times P(B/A)$

Step 3. Calculation

According to the inquiry, $P(healthclub)=10\%=0.10$

$P(atleasttwice/healthclub)=40\%=0.40$

Use the rule of multiplication.

$P(A\cap B)=P\left(A\right)\times P(B/A)$

As a result, the following was obtained:

$P(healthclub\cap atleasttwice)=P(atleasttwice)\times P(healthclub/atleasttwice)$

$=0.10\times 0.40=0.04=4\%$

As a result, $4\%$ of all individuals visit a health club at least twice a week.