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Learn/ A Level Mathematics/ Past Papers/ 2022/ Feb/March 2022 /Paper 5 (Variant 2)

Probability & Statistics 1 — Variant 2

A Level Mathematics · 9709/52 · Feb/March 2022

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
A fair red spinner has edges numbered 1,2,2,31, 2, 2, 3. A fair blue spinner has edges numbered −3,−2,−1,−1-3, -2, -1, -1. Each spinner is spun once and the number on the edge on which each spinner lands is noted. The random variable XX denotes the sum of the resulting two numbers.
1(a) [3]
Draw up the probability distribution table for XX.
1(b) [2]
Given that E(X)=0.25\mathrm{E}(X) = 0.25, find the value of Var(X)\mathrm{Var}(X).
2
In a certain country, the probability of more than 1010 cm of rain on any particular day is 0.180.18, independently of the weather on any other day.
2(a) [3]
Find the probability that in any randomly chosen 77-day period, more than 22 days have more than 1010 cm of rain.
2(b) [3]
For 33 randomly chosen 77-day periods, find the probability that exactly two of these periods have at least one day with more than 1010 cm of rain.

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