At the gym Suppose that 10 % of adults belong to health...

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.

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Key Concepts

Probability

Probability is a measure that quantifies the chance of an event occurring. It is expressed either as a fraction, a decimal between 0 and 1, or as a percentage. This concept forms the basis of understanding how likely events are, and it allows us to assign numerical values to uncertain outcomes.

Conditional Probability

Conditional probability is the probability of one event occurring given that another event has already occurred. It is written as P(B|A), which represents the probability of event B occurring under the condition that event A has occurred. This concept is crucial when dealing with situations where events are dependent on one another.

Multiplication Rule for Probability

The multiplication rule states that the probability of two events occurring together, denoted as P(A and B), is the product of the probability of the first event, P(A), and the conditional probability of the second event given that the first has occurred, P(B|A). This rule is fundamental to calculating joint probabilities in situations where events occur in sequence or are dependent.

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