StudentAidProbability & Statistics 1 — Variant 3
A Level Mathematics · 9709/53 · May/June 2023
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
Two fair coins are thrown at the same time repeatedly until a pair of heads is obtained. The number of throws taken is denoted by the random variable .
1(a)
[1]
State the value of .
1(b)
[1]
Find the probability that exactly throws are required to obtain a pair of heads.
1(c)
[2]
Find the probability that fewer than throws are required to obtain a pair of heads.
2
[5]
Anil is a candidate in an election. He received of the votes. A random sample of voters is chosen. Use an approximation to find the probability that, of the voters, between and inclusive voted for Anil.
3
The random variable takes the values . It is given that , where and are constants.
3(a)
[4]
Given that , find the value of and the value of .
3(b)
[1]
Draw up the probability distribution table for , giving the probabilities as numerical fractions.
3(c)
[2]
Given that , find .
5
Jasmine throws two ordinary fair -sided dice at the same time and notes the numbers on the uppermost faces. The events and are defined as follows. : The sum of the two numbers is less than . : The difference between the two numbers is at most .
5(a)
[4]
Determine whether or not the events and are independent.
5(b)
[3]
Find .
Published by Cambridge Assessment International Education. Reproduced for study use.