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Combined events practice questions with answers

Foundation and Higher · Grade 4 · Non-calculator

A second set of combined events questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

P(A) = 2/10. What is P(not A)? Give a fraction.

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Answer: 4/5

  1. Not A is 1 minus P(A).
  2. The value is 4/5.
  • Method (1): Not A is 1 minus P(A).
  • Accuracy (1): Answer 4/5

Question 2 Easy

A bag has 3 red counters out of 10. One red is taken and not replaced. What is the probability the next counter is also red?

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Answer: 2/9

  1. One red counter has gone.
  2. There are 2 red left out of 9.
  • Method (1): One red counter has gone.
  • Accuracy (1): Answer 2/9

Question 3 Medium

4 boys and 6 girls are in a team. One boy leaves. A student is then picked at random. What is the probability a girl is picked?

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Answer: 2/3

  1. A boy has left.
  2. The girls are still 6.
  • Method (1): A boy has left.
  • Accuracy (1): Answer 2/3

Question 4 Medium

The probability of a prize is 1/4. There are 40 players. How many prizes are expected?

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Answer: 10

  1. Expected number is probability times the count.
  2. The value is 10.
  • Method (1): Expected number is probability times the count.
  • Accuracy (1): Answer 10

Question 5 Hard

P(pass) = 2/5 and the test is taken twice, independently. What is the probability of passing exactly once?

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Answer: 0.48

  1. Pass then fail is 2/5 × 3/5.
  2. There are two orders, so double it.
  • Method (1): Pass then fail is 2/5 × 3/5.
  • Accuracy (1): Answer 0.48

Question 6 Hard

P(A) = 1/5 and P(B) = 1/4, independently. What is the probability that A happens and B does not?

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Answer: 3/20

  1. P(not B) = 3/4.
  2. Multiply by P(A).
  • Method (1): P(not B) = 3/4.
  • Accuracy (1): Answer 3/20

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

A bag has 6 red and 5 blue. One counter is red. It is not replaced. What is the probability the second is blue?

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Answer: 1/2

  1. The first red has been removed.
  2. Blue is still 5 out of the rest.
  • Method (1): The first red has been removed.
  • Accuracy (1): Answer 1/2

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

A fair coin is flipped and a fair 4-sided dice, numbered 1 to 4, is rolled. What is the probability of getting heads and the number 1? Give your answer as a simplified fraction.

  1. 1/8
  2. 3/4
  3. 1/6
Show answer

1/8 The result is 1/8.

Check 2

A bag has 5 red and 6 blue counters. A counter is taken at random, replaced, and then a second counter is taken. What is the probability that both counters are red? Give your answer as a simplified fraction.

  1. 25/121
  2. 10/11
  3. 2/11
Show answer

25/121 The result is 25/121.

Check 3

A bag has 2 red and 6 blue counters. A counter is taken at random and not replaced. A second counter is then taken. What is the probability that both counters are red? Give your answer as a simplified fraction.

  1. 1/28
  2. 1/16
  3. 1/4
Show answer

1/28 The result is 1/28.

Check 4

A fair spinner has 11 equal sections numbered 1 to 11. It is spun twice. What is the probability that both spins give the same number? Give your answer as a simplified fraction.

  1. 1/11
  2. 1/121
  3. 2/11
Show answer

1/11 The result is 1/11.

Check 5

A bag has 2 red and 6 blue counters. A counter is taken at random and replaced. A second counter is then taken. What is the probability that one counter is red and one is blue? Give your answer as a simplified fraction.

  1. 3/8
  2. 3/16
  3. 1/16
Show answer

3/8 The result is 3/8.

Check 6

A fair coin is flipped and a fair 4-sided dice, numbered 1 to 4, is rolled. What is the probability of getting heads and the number 4? Give your answer as a simplified fraction.

  1. 1/8
  2. 3/4
  3. 1/6
Show answer

1/8 The result is 1/8.

Check 7

A bag has 2 red and 3 blue counters. A counter is taken at random, replaced, and then a second counter is taken. What is the probability that both counters are red? Give your answer as a simplified fraction.

  1. 4/25
  2. 4/5
  3. 1/10
Show answer

4/25 The result is 4/25.

Check 8

A bag has 5 red and 2 blue counters. A counter is taken at random and not replaced. A second counter is then taken. What is the probability that both counters are red? Give your answer as a simplified fraction.

  1. 10/21
  2. 25/49
  3. 5/7
Show answer

10/21 The result is 10/21.

Check 9

A fair spinner has 8 equal sections numbered 1 to 8. It is spun twice. What is the probability that both spins give the same number? Give your answer as a simplified fraction.

  1. 1/8
  2. 1/64
  3. 1/4
Show answer

1/8 The result is 1/8.

Check 10

A bag has 5 red and 2 blue counters. A counter is taken at random and replaced. A second counter is then taken. What is the probability that one counter is red and one is blue? Give your answer as a simplified fraction.

  1. 20/49
  2. 10/49
  3. 25/49
Show answer

20/49 The result is 20/49.

Check 11

A fair coin is flipped and a fair 4-sided dice, numbered 1 to 4, is rolled. What is the probability of getting heads and a number greater than 2? Give your answer as a simplified fraction.

  1. 1/4
  2. 1
  3. 1/3
Show answer

1/4 The result is 1/4.

Check 12

A bag has 5 red and 3 blue counters. A counter is taken at random, replaced, and then a second counter is taken. What is the probability that both counters are red? Give your answer as a simplified fraction.

  1. 25/64
  2. 5/4
  3. 5/14
Show answer

25/64 The result is 25/64.

Check 13

A bag has 2 red and 3 blue counters. A counter is taken at random and not replaced. A second counter is then taken. What is the probability that both counters are red? Give your answer as a simplified fraction.

  1. 1/10
  2. 4/25
  3. 2/5
Show answer

1/10 The result is 1/10.

Check 14

A fair spinner has 5 equal sections numbered 1 to 5. It is spun twice. What is the probability that both spins give the same number? Give your answer as a simplified fraction.

  1. 1/5
  2. 1/25
  3. 2/5
Show answer

1/5 The result is 1/5.

Check 15

A bag has 2 red and 3 blue counters. A counter is taken at random and replaced. A second counter is then taken. What is the probability that one counter is red and one is blue? Give your answer as a simplified fraction.

  1. 12/25
  2. 6/25
  3. 4/25
Show answer

12/25 The result is 12/25.

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