surname names
Number Number
Afternoon
Mathematics
🟐 🟐
Advanced
PAPER 31: Statistics
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,
• Answer
centre number and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the spaces provided
• You
– there may 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.
– usemarks
this asfor each as
a guide question
to how are
muchshown
timeintobrackets
spend on each question.
• Read each question carefully before you start to answer it.
Advice
•• Try to answer every question.
Check your answers if you have time at the end.
EDEXCEL A LEVEL MATHEMATICS (9MA0/31) QUESTION PAPER 31
AND MARK SCHEME SUMMER 2025
,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
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, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
(Total for Question 1 is 9 marks)
3
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
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
■■■■
Number Number
Afternoon
Mathematics
🟐 🟐
Advanced
PAPER 31: Statistics
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,
• Answer
centre number and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the spaces provided
• You
– there may 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.
– usemarks
this asfor each as
a guide question
to how are
muchshown
timeintobrackets
spend on each question.
• Read each question carefully before you start to answer it.
Advice
•• Try to answer every question.
Check your answers if you have time at the end.
EDEXCEL A LEVEL MATHEMATICS (9MA0/31) QUESTION PAPER 31
AND MARK SCHEME SUMMER 2025
,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
■■■■
, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
(Total for Question 1 is 9 marks)
3
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
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
■■■■
