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Learn/ A Level Mathematics/ Past Papers/ 2023/ May/June 2023 /Paper 5 (Variant 2)

Probability & Statistics 1 — Variant 2

A Level Mathematics · 9709/52 · May/June 2023

Question Paper

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Mark Scheme

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Questions

2 of 6 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

1
The random variable XX takes the values −2-2, 22 and 33. It is given that P(X=x)=k(x2−1)\mathrm{P}(X = x) = k(x^{2} - 1), where kk is a constant.
1(a) [3]
Draw up the probability distribution table for XX, giving the probabilities as numerical fractions.
1(b) [3]
Find E(X)\mathrm{E}(X) and Var(X)\mathrm{Var}(X).
2
A sports event is taking place for 44 days, beginning on Sunday. The probability that it will rain on Sunday is 0.40.4. On any subsequent day, the probability that it will rain is 0.70.7 if it rained on the previous day and 0.20.2 if it did not rain on the previous day.
2(a) [1]
Find the probability that it does not rain on any of the 44 days of the event.
2(b) [2]
Find the probability that the first day on which it rains during the event is Tuesday.
2(c) [3]
Find the probability that it rains on exactly one of the 44 days of the event.

Published by Cambridge Assessment International Education. Reproduced for study use.