lOMoARcPSD|1286596
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
• Answer 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.
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
, lOMoARcPSD|1286596
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)
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, lOMoARcPSD|1286596
Question 1 continued
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
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_____________________________________________________________________________________
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DO NOT WRITE IN THIS AREA
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 9 marks)
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
• Answer 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.
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
, lOMoARcPSD|1286596
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)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
, lOMoARcPSD|1286596
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)
