Mathematics 9709/53 — May/June 2023

Cambridge A-Level · Probability & Statistics 1 · worked solutions for every part, with the mark scheme

questions

marks

minutes

Topics Discrete Random Variables · The Normal Distribution · Representation of Data · Probability · Permutations and Combinations

Q1Discrete Random VariablesFree sample

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 $X$ .

(a)

State the value of $\mathrm{E}(X)$ .

(b)

Find the probability that exactly 5 throws are required to obtain a pair of heads.

(c)

Find the probability that fewer than 7 throws are required to obtain a pair of heads.

The rest of this paper

6 more questions

Q2The Normal Distribution5M
Q3Discrete Random Variables7M
Q4Representation of Data8M
Q5Probability7M
Q6The Normal Distribution · Discrete Random Variables10M
Q7Permutations and Combinations9M

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