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Learn/ A Level Mathematics/ Past Papers/ 2021/ Feb/March 2021 /Paper 5 (Variant 2)

Probability & Statistics 1 — Variant 2

A Level Mathematics · 9709/52 · Feb/March 2021

Question Paper

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Mark Scheme

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Questions

4 of 7 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 spinner with 55 sides numbered 1,2,3,4,51, 2, 3, 4, 5 is spun repeatedly. The score on each spin is the number on the side on which the spinner lands.
1(a) [1]
Find the probability that a score of 33 is obtained for the first time on the 88th spin.
1(b) [2]
Find the probability that fewer than 66 spins are required to obtain a score of 33 for the first time.
2
Georgie has a red scarf, a blue scarf and a yellow scarf. Each day she wears exactly one of these scarves. The probabilities for the three colours are 0.20.2, 0.450.45 and 0.350.35 respectively. When she wears a red scarf, she always wears a hat. When she wears a blue scarf, she wears a hat with probability 0.40.4. When she wears a yellow scarf, she wears a hat with probability 0.30.3.
2(a) [2]
Find the probability that on a randomly chosen day Georgie wears a hat.
2(b) [3]
Find the probability that on a randomly chosen day Georgie wears a yellow scarf given that she does not wear a hat.
4
The random variable XX takes the values 1,2,3,41, 2, 3, 4 only. The probability that XX takes the value xx is kx(5−x)kx(5 - x), where kk is a constant.
4(a) [2]
Draw up the probability distribution table for XX, in terms of kk.
4(b) [4]
Show that Var(X)=1.05\mathrm{Var}(X) = 1.05.
6
6(a) [2]
Find the total number of different arrangements of the 1111 letters in the word CATERPILLAR.
6(b) [4]
Find the total number of different arrangements of the 1111 letters in the word CATERPILLAR in which there is an R at the beginning and an R at the end, and the two As are not together.
6(c) [4]
Find the total number of different selections of 66 letters from the 1111 letters of the word CATERPILLAR that contain both Rs and at least one A and at least one L.

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