A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2020 · Q17 Marks

It is known that, on average, 1 in 300 flowers of a certain kind are white. A random sample of 200 flowers of this kind is selected.

(a)Use an appropriate approximating distribution to find the probability that more than 1 flower in the sample is white.[3]
(b)Justify the approximating distribution used in part (a).[1]
(c)The probability that a randomly chosen flower of another kind is white is 0.02. A random sample of 150 of these flowers is selected. Use an appropriate approximating distribution to find the probability that the total number of white flowers in the two samples is less than 4.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[B1] Poisson with correct mean stated (to at least 3 sf) or implied in working.
[M1] 1 – P(X= 0 or 1); allow incorrect λ; allow one end error
[A1] SC B1 for use of binomial or no working shown leading to correct final answer.
[B1] Accept p or np clearly stated in part (a). Do not accept n is large and p is small.
[B1] Poisson with correct mean stated (to at least 3sf) or implied in working.
[M1] P(X= 0, 1, 2, 3); allow incorrect λ; allow one end error. Must not be multiplied by any additional values.
[A1] As final answer.

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