GCSE Maths · Topic guide

Probability

Probability measures how likely an event is to happen, given as a number between 0 (impossible) and 1 (certain), often written as a fraction, decimal or percentage.

Grade 3-4 (Foundation)Topic 2.12

Before you start

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Method

  1. For equally likely outcomes, probability = (number of favourable outcomes) divided by (total number of possible outcomes).
  2. The probabilities of all possible outcomes in a situation always add up to 1.
  3. The probability of an event NOT happening is 1 minus the probability of it happening.
  4. For two independent events happening together (AND), multiply their probabilities; for one event OR another mutually exclusive event, add their probabilities.
  5. Use a sample space diagram, table, tree diagram or Venn diagram to organise more complex situations before calculating.

Worked example

A bag contains 4 red, 3 blue and 5 green counters. A counter is picked at random. Find the probability it is (a) blue, (b) not green.

  1. Find the total number of counters: 4 + 3 + 5 = 12.
  2. (a) There are 3 blue counters, so P(blue) = 3/12, which simplifies to 1/4.
  3. (b) There are 5 green counters, so P(green) = 5/12.
  4. P(not green) = 1 - P(green) = 1 - 5/12 = 7/12.

Practice questions

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Exam-style questions

Written in the style of a GCSE exam paper, with a full mark scheme.

Q1[3 marks]

A box contains only red pens and blue pens. The probability of picking a red pen at random is 0.35. There are 60 pens in the box. Work out the number of blue pens.

Q2[4 marks]

A fair spinner is split into red, blue and green sections. P(red) = 0.4 and P(blue) = 0.25. The spinner is spun twice. Work out the probability that both spins land on green.

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