Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Luttley College has a very large student population. $60\%$ of the students are boys. On Friday afternoons, each student may select exactly one of Games, Drama or Music. It is found that $75\%$ of the boys choose Games, $10\%$ choose Drama, and the rest choose Music. For the girls, $30\%$ choose Games, $55\%$ choose Drama, and the remainder choose Music.
(i)[3]

$6$ boys are selected at random. Calculate the probability that fewer than $3$ of them choose Music.

(ii)[6]

$5$ Drama students are selected at random. Calculate the probability that at least $1$ of them is a boy.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: The probabilities $0.15$ and $0.85$ are both identified correctly

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