Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

A box has $3$ red balls and $5$ white balls. A ball is taken at random from the box and is not put back. Then a second ball is taken at random from the box.
(i)[1]

Determine the probability that both balls selected are red.

(ii)[2]

Show that the probability that the balls selected have different colours is $\frac{15}{28}$.

(iii)[2]

Given that the second ball chosen is red, determine the probability that the first ball chosen is red.

(iv)[2]

The random variable $X$ stands for the number of red balls selected. Construct the probability distribution table for $X$.

(v)[3]

Calculate $\mathrm{Var}(X)$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct probability is $\frac{3}{8} \times \frac{2}{7} = \frac{3}{28}$

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