Probability
Probability is a measure, from 0 to 1, of how likely an event is to happen, where 0 means impossible and 1 means certain. Probabilities can be written as fractions, decimals or percentages, and are found using equally likely outcomes, two-way tables, sample space diagrams or experimental data. This topic underpins probability questions found throughout GCSE maths.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify all the possible equally likely outcomes for the situation (the sample space).
- Write the probability of a single event as (number of favourable outcomes) divided by (total number of outcomes), fully simplified.
- Remember that every probability lies between 0 (impossible) and 1 (certain), and that the probabilities of all possible outcomes of an experiment sum to 1.
- For combined 'and' (independent) events, multiply the individual probabilities; for combined 'or' (mutually exclusive) events, add the individual probabilities.
- Use relative frequency (frequency divided by number of trials) to estimate a probability from experimental or survey data.
- Organise combined events with a sample space diagram, two-way table or tree diagram before calculating probabilities from them.
Worked example
A bag contains 15 counters: 6 yellow, 5 purple and 4 orange. A counter is picked at random, its colour is noted, then it is put back before a second counter is picked at random. (a) Find the probability that the first counter is purple. (b) Find the probability that both counters picked are orange.
- There are 15 counters in total, so P(first counter purple) = 5/15.
- Simplify 5/15 by dividing the numerator and denominator by 5 to get 1/3.
- Since the counter is replaced before the second pick, the two picks are independent, so multiply their individual probabilities.
- P(orange) on a single pick = 4/15.
- P(both counters orange) = 4/15 x 4/15 = 16/225.
Practice questions
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Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A fair six-sided dice, numbered 1 to 6, is rolled once. Find P(rolling a factor of 6).
A biased spinner lands on red, blue or green only. P(red) = 0.3 and P(blue) = 0.45. The spinner is spun 200 times. Work out the expected number of times it lands on green.
A drawer contains 9 socks: 5 black and 4 white. Two socks are taken out at random, one after another, without replacement. Find the probability that the two socks are different colours.
Free printable worksheet
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