Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Thursday 19 June 2025
Afternoon Paper
reference 9MA0/31
Mathematics
Advanced
PAPER 31: Statistics
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by Pearson regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• – there may
Answer
labelled.
the questions in the spaces provided
• You be more space than you need.
should show sufficient working to make your methods clear.
• Values
Answers without working may not gain full credit.
from statistical tables should be quoted in full. If a calculator is used instead of
• Inexact answers should be given to three significant figures unless otherwise stated.
tables the value should be given to an equivalent degree of accuracy.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The total mark for this part of the examination is 50. There are 6 questions.
marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end.
Try to answer every question.
Turn over
P75695A
©2025 Pearson Education Ltd.
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*P75695A0120*
,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
.................... 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.
(c) Find the exact value of P(W | X )
(2)
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2
*P75695A0220*
, Question 1 continued
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(Total for Question 1 is 9 marks)
3
*P75695A0320* Turn over
, 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
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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.
(2)
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4
*P75695A0420*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Thursday 19 June 2025
Afternoon Paper
reference 9MA0/31
Mathematics
Advanced
PAPER 31: Statistics
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by Pearson regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• – there may
Answer
labelled.
the questions in the spaces provided
• You be more space than you need.
should show sufficient working to make your methods clear.
• Values
Answers without working may not gain full credit.
from statistical tables should be quoted in full. If a calculator is used instead of
• Inexact answers should be given to three significant figures unless otherwise stated.
tables the value should be given to an equivalent degree of accuracy.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The total mark for this part of the examination is 50. There are 6 questions.
marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end.
Try to answer every question.
Turn over
P75695A
©2025 Pearson Education Ltd.
Y:1/1/1/1/
*P75695A0120*
,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 DO NOT WRITE IN THIS AREA 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
.................... 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.
(c) Find the exact value of P(W | X )
(2)
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2
*P75695A0220*
, Question 1 continued
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(Total for Question 1 is 9 marks)
3
*P75695A0320* Turn over
, 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 DO NOT WRITE IN THIS AREA 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.
(2)
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4
*P75695A0420*
