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GCSE Mathematics  ›  M5.1 Basic probability and sample space

Basic probability and sample space

Free AQA GCSE Mathematics practice questions on Basic probability and sample space. Sample questions below with detailed mark schemes — sign up to practise the full set with spaced repetition.

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State — 2 marks

A physics teacher has a bag containing coloured balls to demonstrate probability concepts. The bag contains 3 red balls, 5 blue balls, and 2 green balls. All balls are identical except for their colour.

  1. State the total number of possible outcomes when one ball is drawn from the bag. [1 mark]
  2. State the number of favourable outcomes for drawing a blue ball. [1 mark]
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Show — 4 marks

A physics teacher carries out an experiment using a fair six-sided die and a spinner divided into three equal sections coloured red, blue and yellow. Students need to roll the die once and spin the spinner once to determine which practical activity they will complete.

  1. Show that the total number of possible outcomes when rolling the die once and spinning the spinner once is 18. [1 mark]
  2. A student rolls the die and spins the spinner. Show all the possible outcomes that result in an even number on the die AND the colour red on the spinner. [2 marks]
  3. Using your answer to part (b), show that the probability of obtaining an even number AND red is 1/6. [1 mark]
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Calculate — 2 marks

A bag contains 20 cards numbered from 1 to 20. Priya picks one card at random.

  1. (01.1) Calculate the probability that Priya picks a card with an even number. [1 mark]
  2. (01.2) Calculate the probability that Priya picks a card with a number greater than 15. [1 mark]
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  • (01.1) 10/20 or 1/2 or 0.5 or 50%
  • (01.2) 5/20 or 1/4 or 0.25 or 25%

Explain — 2 marks

A fair spinner is divided into 8 equal sectors numbered 1 to 8.

  1. (01.1) Write down all the possible outcomes when the spinner is spun once. [1 mark]
  2. (01.2) Explain why the probability of landing on a number greater than 6 is 1/4. [1 mark]
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  • (01.1) 1, 2, 3, 4, 5, 6, 7, 8 (accept any order)
  • (01.2) There are 2 numbers greater than 6 (7 and 8) out of 8 possible outcomes
  • (01.2) 2/8 = 1/4

Calculate — 5 marks

A bag contains 12 identical counters. There are 5 red counters, 4 blue counters and 3 green counters. Kieran takes two counters at random from the bag without replacement.

  1. (01.1) Calculate the probability that both counters are red. [2 marks]
  2. (01.2) Calculate the probability that the two counters are different colours. [3 marks]
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  • (01.1) 5/12 × 4/11 or equivalent fraction multiplication
  • (01.1) 20/132 or 5/33 or equivalent simplified fraction
  • (01.2) Correct method to find probability of same colour (e.g., 20/132 + 12/132 + 6/132 or equivalent)
  • (01.2) Correct calculation of P(same colour) = 38/132 or 19/66
  • (01.2) Correct final answer: 94/132 or 47/66 or equivalent

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