A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2019 · Q610 Marks

A box contains 3 red balls and 5 white balls. One ball is chosen at random from the box and is not returned to the box. A second ball is now chosen at random from the box.

(i)Find the probability that both balls chosen are red.[1]
(ii)Show that the probability that the balls chosen are of different colours is 15/28.[2]
(iii)Given that the second ball chosen is red, find the probability that the first ball chosen is red.[2]
(iv)The random variable X denotes the number of red balls chosen. Draw up the probability distribution table for X.[2]
(v)Find Var(X).[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[B1] 3/8 × 2/7 = 3/28 OE
[M1] Method shown, numerical calculations identified, may include replacements
[A1] AG, Fully correct calculations
[M1] Method shown, numerical calculations identified, may include replacements
[A1] AG, Fully correct calculations
[M1] Conditional probability formula used consistent with their probabilities or correct
[A1] OE
[B1] Probability distribution table with correct values of x and at least one correct probability placed. Extra x values allowed with probability of zero stated.
[B1FT] Fully correct FT P(2) = their (i), P(1) = their (ii), Σ(p) = 1.
[B1] May be implied by use in variance formula
[M1] Substitute into correct variance formula, must have ' - their mean²' Must be for 2 or more non-zero x-values
[A1] Correct final answer

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