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Learn/ A Level Mathematics/ Past Papers/ 2024/ May/June 2024 /Paper 5 (Variant 2)

Probability & Statistics 1 — Variant 2

A Level Mathematics · 9709/52 · May/June 2024

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
Rajesh applies once every year for a ticket to a music festival. The probability that he is successful in any particular year is 0.30.3, independently of other years.
1(a) [1]
Find the probability that Rajesh is successful for the first time on his 7th attempt.
1(b) [2]
Find the probability that Rajesh is successful for the first time before his 6th attempt.
1(c) [2]
Find the probability that Rajesh is successful for the second time on his 10th attempt.
2
Seva has a coin which is biased so that when it is thrown the probability of obtaining a head is 13\frac{1}{3}. He also has a bag containing 4 red marbles and 5 blue marbles. Seva throws the coin. If he obtains a head, he selects one marble from the bag at random. If he obtains a tail, he selects two marbles from the bag at random and without replacement.
2(a) [3]
Find the probability that Seva selects at least one red marble.
2(b) [2]
Find the probability that Seva obtains a head given that he selects no red marbles.
3
The weights of oranges can be modelled by a normal distribution with mean 131131 grams and standard deviation 5454 grams. Oranges are classified as small, medium or large. A large orange weighs at least 184184 grams and 20%20\% of oranges are classified as small.
3(a) [3]
Find the percentage of oranges that are classified as large.
3(b) [3]
Find the greatest possible weight of a small orange.
5
Jasmine has one $5\$5 coin, two $2\$2 coins and two $1\$1 coins. She selects two of these coins at random. The random variable XX is the total value, in dollars, of these two coins.
5(a) [1]
Show that P(X=7)=0.2P(X = 7) = 0.2.
5(b) [3]
Draw up the probability distribution table for XX.
5(c) [3]
Find the value of Var(X)\mathrm{Var}(X).
6
The residents of Mahjing were asked to classify their local bus service: 25%25\% of residents classified their service as good. 60%60\% of residents classified their service as satisfactory. 15%15\% of residents classified their service as poor.
6(a) [5]
A random sample of 110 residents of Mahjing is chosen. Use a suitable approximation to find the probability that fewer than 22 residents classified their bus service as good.
6(b) [3]
For a random sample of 10 residents of Mahjing, find the probability that fewer than 8 classified their bus service as good or satisfactory.
6(c) [2]
Three residents of Mahjing are selected at random. Find the probability that one resident classified the bus service as good, one as satisfactory and one as poor.
7
7(a) [1]
How many different arrangements are there of the 10 letters in the word REGENERATE?
7(b) [4]
How many different arrangements are there of the 10 letters in the word REGENERATE in which the 4 Es are together and the 2 Rs have exactly 3 letters in between them?
7(c) [5]
Find the probability that a randomly chosen arrangement of the 10 letters in the word REGENERATE is one in which the consonants (G, N, R, R, T) and vowels (A, E, E, E, E) alternate, so that no two consonants are next to each other and no two vowels are next to each other.

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