Edexcel A Level In GCE mathematics (9MA0/31) Options 31:statistics + mark scheme June
2025
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 andatcandidate
the top ofnumber.
this page with your name,
• Answer
centre 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
•• AThThebooklet
e total
‘Mathematical Formulae and Statistical Tables’ is provided.
for efor
ma r ksmark achthis
qu epart
stionofathe
re sexamination
hown in bracis
ke50.
ts There are 6 questions.
– use this as a guide as to how much time to spend on each question.
•
Y:1/1/1/1/
AdRveicaed each question carefully before you start to answer it.
•• Try to answer every question.
Check your answers if you have time at the end.
P75695A
©2025 Pearson Education Ltd.
,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
■■
, Question 1 continued
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 1 is 9 marks)
3
■■ Turn over
2025
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 andatcandidate
the top ofnumber.
this page with your name,
• Answer
centre 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
•• AThThebooklet
e total
‘Mathematical Formulae and Statistical Tables’ is provided.
for efor
ma r ksmark achthis
qu epart
stionofathe
re sexamination
hown in bracis
ke50.
ts There are 6 questions.
– use this as a guide as to how much time to spend on each question.
•
Y:1/1/1/1/
AdRveicaed each question carefully before you start to answer it.
•• Try to answer every question.
Check your answers if you have time at the end.
P75695A
©2025 Pearson Education Ltd.
,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
■■
, Question 1 continued
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 1 is 9 marks)
3
■■ Turn over
