Syllabus Edition

First teaching 2023

First exams 2025

|

Probability Diagrams - Tree & Venn Diagrams (CIE IGCSE Maths: Extended)

Exam Questions

2 hours28 questions
1a
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2 marks

On any Saturday, the probability that Arun plays football is 3 over 4.
On any Saturday, the probability that Bob plays football is 2 over 5.

Complete the tree diagram.

cie-igcse-2020-may-jun-p4-tz3-q7ai

1b
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2 marks

Calculate the probability that, one Saturday, Arun and Bob both play football.

1c
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3 marks

Calculate the probability that, one Saturday, either Arun plays football or Bob plays football, but not both.

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2
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3 marks

A soccer team plays two matches.
The tree diagram shows the probability of the team winning or losing the matches. 

cie-igcse-q22-tree-diagram

Find the probability that the soccer team wins at least one of the two matches.

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3a
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2 marks

calligraphic E equals{students in a school}
F equals{students who play football}
B equals{students who play baseball}
 
There are 240 students in the school.
 
• 120 students play football
• 40 students play baseball 
• 90 students play football but not baseball.

Complete the Venn diagram to show this information.
 

cie-igcse-2019-may-jun-p4-tz1-q6a 

3b
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1 mark

A student in the school is chosen at random.
 
Find the probability that this student plays baseball but not football.

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4
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2 marks

The Venn diagram below shows information about the number of gardeners who grow melons (M ), potatoes (P ) and carrots (C ).

cie-igcse-2019-may-jun-p2-tz2-q21b

A gardener is chosen at random from the gardeners who grow melons.
 
Find the probability that this gardener does not grow carrots.

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5
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2 marks

At a fitness centre, the number of members using the exercise machines (E), the swimming pool (S) and the tennis courts (T) is shown on the Venn diagram.

cie-igcse-2018-may-jun-1-p4-q10c

A member using the swimming pool is chosen at random.

Find the probability that this member also uses the tennis courts and the exercise machines.

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1a
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2 marks

Tanya plants some seeds.
The probability that a seed will produce flowers is 0.8.
When a seed produces flowers, the probability that the flowers are red is 0.6 and the probability that the flowers are yellow is 0.3.

Complete the tree diagram.

cie-igcse-2020-may-jun-p4-tz2-q7bi 

1b
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2 marks

Find the probability that a seed chosen at random produces red flowers.

1c
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3 marks

Tanya chooses a seed at random.
 
Find the probability that this seed does not produce red flowers and does not produce yellow flowers.

1d
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3 marks

Two of the seeds are chosen at random.
 
Find the probability that one produces flowers and one does not produce flowers.

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2a
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1 mark

40 children were asked if they have a computer or a phone or both.
The Venn diagram shows the results.

cie-igcse-2019-may-jun-p2-tz3-q20ai

A child is chosen at random from the children who have a computer.
 
Write down the probability that this child also has a phone.

2b
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2 marks

Complete the Venn diagram.
 

cie-igcse-2019-may-jun-p2-tz3-q20aii

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3a
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3 marks

The Venn diagram shows information about the number of elements in sets A, B and calligraphic E.
cie-igcse-2018-may-jun-2-p2-q23

straight n left parenthesis A union B right parenthesis equals 23

Find the value of x.

x equals................................................

3b
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2 marks

An element is chosen at random from calligraphic E.

Find the probability that this element is in left parenthesis A union B right parenthesis apostrophe.

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4a
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2 marks

Items made at a factory have to pass two checks.

90% pass the first check.
The items that fail are scrapped.
99% of the items that pass the first check pass the second check.
The items that fail are scrapped.

Complete the tree diagram.

q19a-paper-1h-nov-2021-aqa-gcse-maths

4b
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3 marks

An item is chosen at random before the checks.

Work out the probability that the item is scrapped.

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1a
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2 marks

Harris is taking a driving test.
The probability that he passes the driving test at the first attempt is 0.6.
If he fails, the probability that he passes at any further attempt is 0.75.

Calculate the probability that Harris passes the driving test at the second attempt.

1b
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2 marks

Calculate the probability that Harris takes no more than three attempts to pass the driving test.

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2a
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1 mark

The probability that Andrei cycles to school is r.

Write down, in terms of r, the probability that Andrei does not cycle to school. 

2b
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8 marks

The probability that Benoit does not cycle to school is 1.3 minus r.
The probability that both Andrei and Benoit do not cycle to school is 0.4.

i)
Complete the equation in terms of r.
 
 left parenthesis......................... right parenthesis space cross times space left parenthesis......................... right parenthesis space equals space 0.4  
 
[1]
ii)
Show that this equation simplifies to 10 r squared minus 23 r plus 9 equals 0. 
 
[3]
iii)
Solve by factorisation 10 r squared minus 23 r plus 9 equals 0. 
 
r = ................... or r = ................... [3]
iv)
Find the probability that Benoit does not cycle to school. 
 
[1]

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3a
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2 marks

Anna plays a game with an ordinary, fair dice.

If she rolls 1 she wins.
If she rolls 2 or 3 she loses.
If she rolls 4, 5 or 6 she rolls again.

When she has to roll again,

if she rolls an odd number she wins
if she rolls an even number she loses.

Complete the tree diagram with the four missing probabilities.

q6a-paper-1h-june-2019-aqa-gcse-maths

3b
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4 marks

Is Anna more likely to win or to lose?

You must work out the probability that she wins.

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4a
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2 marks

On Friday, Greg takes part in a long jump competition.
He has to jump at least 7.5 metres to qualify for the final on Saturday.

  • He has up to three jumps to qualify.
  • If he jumps at least 7.5 metres he does not jump again on Friday.

Each time Greg jumps, the probability he jumps at least 7.5 metres is 0.8
Assume each jump is independent.

Complete the tree diagram.

First jump Second jump Third jump

q20a-paper1h-specimen2015-aqa-gcse-maths

4b
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2 marks

Work out the probability that he does not need the third jump to qualify.

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