A LEVEL MATHEMATICS: Actual June 2025 PAST PAPER 3: Statistics. All Assessment
Questions & Mark Scheme [Edexcel 9MA0/31]
Exam Resource Summary
The June 2025 Pearson Edexcel A Level Mathematics (9MA0) – Paper 31: Statistics – Merged Question Paper
& Mark Scheme document brings together the official examination paper with its full mark scheme. This paper
assesses students’ understanding of statistical methods and applications—including probability distributions,
hypothesis testing, correlation and regression, statistical modelling and interpretation of results. The merged
format presents each question followed by its corresponding marking criteria, offering full transparency of
examiner expectations, mark allocation, and answer structure. This resource is essential for targeted revision,
self‐assessment, and mastery of statistical skills required for the June 2025 Edexcel A Level Mathematics Paper
31 examination.
Turn over
,1. Bag A contains 5 red, 4 yellow and 3 green beads.
Bag B only contains red and yellow beads.
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A bead is selected at random from bag A and a second bead is selected at random from
bag B
3
Given that the probability that both beads selected are yellow is
16
(a) (i) find the probability of selecting a yellow bead from bag B
(2)
(ii) Hence complete the tree diagram below by finding the probability on
each branch.
Bag A Bag B
.................... red
red
....................
yellow
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....................
.................... red
....................
yellow
.................... yellow
.................... red
....................
green
.................... yellow
(2)
(b) Find the exact probability that at least one of the two beads selected is yellow.
(3)
The event X is that at least one of the beads selected is yellow.
The event W is that a green bead is selected.
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(c) Find the exact value of P(W | X )
(2)
2
■■■■
, 2. Runners in an athletics club can train with either coach A or coach B for the 400 m race.
Coach A trains 120 runners for the 400 m and records the best time, x seconds, for
DO NOT WRITE IN THIS AREA
each runner.
The results are summarised by the following statistics
x 6612 x 2
364902
(a) Calculate the mean of the best times for the runners trained by coach A
(1)
(b) Calculate the standard deviation of the best times for the runners trained by coach A
(2)
The mean and standard deviation for the best times of the 100 runners trained for
the 400 m by coach B are 55.1 seconds and 3.6 seconds respectively.
A 400 m race consists of equal numbers of the fastest runners trained by coach A and by
coach B
(c) State, giving a reason, which coach is more likely to have trained the winner.
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(2)
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4
■■■■
Questions & Mark Scheme [Edexcel 9MA0/31]
Exam Resource Summary
The June 2025 Pearson Edexcel A Level Mathematics (9MA0) – Paper 31: Statistics – Merged Question Paper
& Mark Scheme document brings together the official examination paper with its full mark scheme. This paper
assesses students’ understanding of statistical methods and applications—including probability distributions,
hypothesis testing, correlation and regression, statistical modelling and interpretation of results. The merged
format presents each question followed by its corresponding marking criteria, offering full transparency of
examiner expectations, mark allocation, and answer structure. This resource is essential for targeted revision,
self‐assessment, and mastery of statistical skills required for the June 2025 Edexcel A Level Mathematics Paper
31 examination.
Turn over
,1. Bag A contains 5 red, 4 yellow and 3 green beads.
Bag B only contains red and yellow beads.
DO NOT WRITE IN THIS AREA
A bead is selected at random from bag A and a second bead is selected at random from
bag B
3
Given that the probability that both beads selected are yellow is
16
(a) (i) find the probability of selecting a yellow bead from bag B
(2)
(ii) Hence complete the tree diagram below by finding the probability on
each branch.
Bag A Bag B
.................... red
red
....................
yellow
DO NOT WRITE IN THIS AREA
....................
.................... red
....................
yellow
.................... yellow
.................... red
....................
green
.................... yellow
(2)
(b) Find the exact probability that at least one of the two beads selected is yellow.
(3)
The event X is that at least one of the beads selected is yellow.
The event W is that a green bead is selected.
DO NOT WRITE IN THIS AREA
(c) Find the exact value of P(W | X )
(2)
2
■■■■
, 2. Runners in an athletics club can train with either coach A or coach B for the 400 m race.
Coach A trains 120 runners for the 400 m and records the best time, x seconds, for
DO NOT WRITE IN THIS AREA
each runner.
The results are summarised by the following statistics
x 6612 x 2
364902
(a) Calculate the mean of the best times for the runners trained by coach A
(1)
(b) Calculate the standard deviation of the best times for the runners trained by coach A
(2)
The mean and standard deviation for the best times of the 100 runners trained for
the 400 m by coach B are 55.1 seconds and 3.6 seconds respectively.
A 400 m race consists of equal numbers of the fastest runners trained by coach A and by
coach B
(c) State, giving a reason, which coach is more likely to have trained the winner.
DO NOT WRITE IN THIS AREA
(2)
DO NOT WRITE IN THIS AREA
4
■■■■
