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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1 mark

On any day the probability that it rains is 1 third.

When it rains the probability that Amira goes fishing is 3 over 5.
When it does not rain the probability that Amira goes fishing is 3 over 4.

In a period of 60 days on how many days is it expected to rain?

1b
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2 marks

Complete the tree diagram.

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1c
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3 marks

Find the probability that on any day Amira goes fishing.

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2a
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2 marks

A bag contains 15 red beads and 10 yellow beads.
Ariana picks a bead at random, records its colour and replaces it in the bag.
She then picks another bead at random.

Find the probability that she picks two red beads.

2b
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1 mark

Find the probability that she does not pick two red beads.

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3a
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4 marks

calligraphic E space equals space{odd numbers less than 30}
A space equals space{3, 9, 15, 21, 27}
B space equals space{5, 15, 25}

Complete the Venn diagram to represent this information.

q5a-5-2-medium-edexcel-gcse-maths

3b
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2 marks

A number is chosen at random from the universal set, calligraphic E.

What is the probability that the number is in the set A space union space B?

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4a
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2 marks

Here is a Venn diagram.

q6a-5-2-medium-edexcel-gcse-maths

Write down the numbers that are in set

i) A space union space B

[1]

ii) A space intersection space B

[1]

4b
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2 marks

One of the numbers in the diagram is chosen at random.

Find the probability that the number is in set A apostrophe.

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5a
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2 marks

The numbers from 1 to 14 are shown in the Venn diagram.

q1-paper1h-nov2020-edexcel-igcse-maths

i)
List the members of the set A intersection B

[1]

ii)
List the members of the set B ʹ 

[1]

5b
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2 marks

A number is picked at random from the numbers in the Venn diagram.

Find the probability that this number is in set Abut is not in set B.

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6
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2 marks

A and B are two events.

Some probabilities are shown on the Venn diagram.

q14-paper-1h-nov-2018-aqa-gcse-maths-1

Work out straight P left parenthesis straight A apostrophe union straight B right parenthesis.

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1a
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2 marks

There are 32 students in a class.

5 do not study any languages.
15 study German (G).
18 study Spanish (S).

cie-igcse-2020-oct-nov-p4-tz1-q9a

Complete the Venn diagram to show this information.

1b
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1 mark

A student is chosen at random.
 
Find the probability that the student studies Spanish but not German.

1c
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1 mark

A student who studies German is chosen at random.

Find the probability that this student also studies Spanish.

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2a
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3 marks

On any Saturday, the probability that Bob plays football is 2 over 5.
 
Calculate the probability that Bob plays football for 2 of the next 3 Saturdays.

2b
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2 marks

On any Saturday, the probability that Arun plays football is 3 over 4.
When Arun plays football, the probability that he scores the winning goal is 1 over 7.
 
Calculate the probability that Arun scores the winning goal one Saturday.

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3a
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2 marks

Machine A and machine B make bottles.

The probability that a bottle made by machine A is faulty is 0.02
The probability that a bottle made by machine B is faulty is 0.05

Complete the probability tree diagram.

q3a-5-3-high-edexcel-gcse-maths

3b
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3 marks

Shazia takes at random one bottle made by machine A and one bottle made by machine B.

Work out the probability that at least one of these bottles is faulty.

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4a
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2 marks

A darts team is going to play a match on Saturday and on Sunday.
The probability that the team will win on Saturday is 0.45

If they win on Saturday, the probability that they will win on Sunday is 0.67
If they do not win on Saturday, the probability that they will win on Sunday is 0.35

Complete the probability tree diagram.

q5a-5-2-high-edexcel-gcse-maths

4b
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3 marks

Find the probability that the team will win exactly one of the two matches.

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5a
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1 mark

Two ordinary fair dice are rolled.

Complete the tree diagram.

q11a-paper-2h-june-2018-aqa-gcse-maths

5b
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1 mark

Work out the probability that both dice land on a number less than 3.

5c
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2 marks

Work out the probability that exactly one of the dice lands on a number less than 3.

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1
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3 marks

cie-igcse-2020-oct-nov-p4-tz2-q6a

The diagram shows six discs.
Each disc has a colour and a number.

Two of the six discs are picked at random with replacement.

Find the probability that both discs have the same colour.

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2
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3 marks

The probability that the school bus is late is 9 over 10.
If the school bus is late, the probability that Seb travels on the bus is 15 over 16.
If the school bus is on time, the probability that Seb travels on the bus is 3 over 4.

Find the probability that Seb travels on the bus.

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3a
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3 marks

The probability that it will rain tomorrow is 5 over 8.
If it rains, the probability that Rafael walks to school is 1 over 6.
If it does not rain, the probability that Rafael walks to school is 7 over 10.

Complete the tree diagram.
cie-igcse-2018-may-jun-1-p4-q9a

3b
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2 marks

Calculate the probability that it will rain tomorrow and Rafael walks to school.

3c
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3 marks

Calculate the probability that Rafael does not walk to school.

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4a
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2 marks

Box A and box B each contain blue and green pens only.
Raphael picks a pen at random from box A and Paulo picks a pen at random from box B.
The probability that Raphael picks a blue pen is 2 over 3.
The probability that both Raphael and Paulo pick a blue pen is 8 over 15.

Find the probability that Paulo picks a blue pen.

4b
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3 marks

Find the probability that both Raphael and Paulo pick a green pen.

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