## Exam-Style Question on Probability## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 688. This question is similar to one that appeared on an IB AA Higher paper in 2021. The use of a calculator is allowed.

At a fitness club, \( 60\% \) of the members are full-time members, and \( 30\% \) of the members participate in group fitness classes. \( 25\% \) of the members are neither full-time members nor participate in group fitness classes.

A member is selected at random.

(a) Find the probability that the member is a full-time member and participates in group fitness classes.

(b) Find the probability that the member participates in group fitness classes, but is not a full-time member.

In the club, \( 50\% \) of the members are male, and \( 40\% \) of the male members participate in group fitness classes.

A member is selected at random. Let \( M \) be the event "the member is male" and let \( F \) be the event "the member participates in group fitness classes".

(c) Find \( P(M \cap F) \).

(d) Determine if the events \( M \) and \( F \) are independent. Justify your answer.

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