N2024 P2 Q6

A sports club has three categories of membership. There are \(27\) Youth members, \(45\) Adult members and \(18\) Senior members.

The club secretary wishes to find out the opinions of members of the club about the facilities offered. She gives a questionnaire to all the members of the club. She receives replies from \(65\) of the members.

1. Explain whether the \(65\) members comprise a sample or a population.[1]

The secretary decides to form a committee of members to discuss the results of her questionnaire.

2. Explain an advantage of choosing a random sample of members for her committee.[1]

The secretary decides that the committee will consist of \(6\) randomly chosen members, but there will be:

• at least \(1\) member from each category

• more Adult members than Youth members and

• more Adult members than Senior members.

3. Find the probability that the committee contains more Youth members than Senior members.[4]