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Learn/ A Level Mathematics/ Past Papers/ 2022/ May/June 2022 /Paper 5 (Variant 2)

Probability & Statistics 1 — Variant 2

A Level Mathematics · 9709/52 · May/June 2022

Question Paper

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Questions

6 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 [3]
For nn values of the variable xx, it is given that Σ(x−200)=446\Sigma(x - 200) = 446 and Σx=6846\Sigma x = 6846. Find the value of nn.
2
A fair 66-sided die has the numbers 1,2,2,3,3,31, 2, 2, 3, 3, 3 on its faces. The die is rolled twice. The random variable XX denotes the sum of the two numbers obtained.
2(a) [3]
Draw up the probability distribution table for XX.
2(b) [3]
Find E(X)\mathrm{E}(X) and Var(X)\mathrm{Var}(X).
4
The weights, in kg, of bags of rice produced by Anders have the distribution N(2.02,0.032)\mathrm{N}(2.02, 0.03^{2}).
4(a) [3]
Find the probability that a randomly chosen bag of rice produced by Anders weighs between 1.981.98 and 2.032.03 kg. The weights of bags of rice produced by Binders are normally distributed with mean 2.552.55 kg and standard deviation σ\sigma kg. In a random sample of 50005000 of these bags, 134134 weighed more than 2.62.6 kg.
4(b) [4]
Find the value of σ\sigma.
5
In a large college, 28%28\% of the students do not play any musical instrument, 52%52\% play exactly one musical instrument and the remainder play two or more musical instruments. A random sample of 1212 students from the college is chosen.
5(a) [3]
Find the probability that more than 99 of these students play at least one musical instrument. A random sample of 9090 students from the college is now chosen.
5(b) [5]
Use an approximation to find the probability that fewer than 4040 of these students play exactly one musical instrument.
6
6(a) [1]
Find the number of different arrangements of the 99 letters in the word CROCODILE.
6(b) [3]
Find the number of different arrangements of the 99 letters in the word CROCODILE in which there is a CC at each end and the two OOs are not together.
6(c) [3]
Four letters are selected from the 99 letters in the word CROCODILE. Find the number of selections in which the number of CCs is not the same as the number of OOs.
6(d) [3]
Find the number of ways in which the 99 letters in the word CROCODILE can be divided into three groups, each containing three letters, if the two CCs must be in different groups.
7
Hanna buys 1212 hollow chocolate eggs that each contain a sweet. The eggs look identical but Hanna knows that 33 contain a red sweet, 44 contain an orange sweet and 55 contain a yellow sweet. Each of Hanna's three children in turn randomly chooses and eats one of the eggs, keeping the sweet it contained.
7(a) [4]
Find the probability that all 33 eggs chosen contain the same colour sweet.
7(b) [2]
Find the probability that all 33 eggs chosen contain a yellow sweet, given that all three children have the same colour sweet.
7(c) [3]
Find the probability that at least one of Hanna's three children chooses an egg that contains an orange sweet.

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