GCSE Maths revision · Probability and statistics

Relative frequency

Foundation and Higher

The idea

The probabilities of all the possible outcomes add up to $1$ . Relative frequency, $\frac{\text{times it happened}}{\text{number of trials}}$ , estimates a probability from an experiment, and more trials give a better estimate.

To find a missing probability, subtract the others from $1$ .
For relative frequency, divide the frequency by the total trials.
Compare with the theoretical probability to judge whether a dice or spinner is fair.

Watch out A probability can never be bigger than $1$ .

See it worked

Worked exampleNon-calculator2 marks

A machine selects one of three symbols: a star, a circle or a square. The probability of a star is 0.28 and the probability of a circle is 0.47. What is the probability of a square?

$1-0.28-0.47$
Probabilities of all possible outcomes add to 1.
P(square) = 1 $-$ (0.28 + 0.47) = 0.25.

Answer 0.25

Your turn

Question 1Non-calculator2 marks

A drawing pin is dropped 150 times. It lands point up 57 times. Use these results to estimate the probability that it lands point down on the next drop. Give your answer as a decimal.

Question 2Non-calculator3 marks

A spinner numbered 1, 2 and 3 is spun 60 times. It lands on 1 twelve times, on 2 eighteen times and on 3 thirty times.

(a) Work out the relative frequency of the spinner landing on 3.

(b) The spinner is spun 300 more times. Work out an estimate for the number of times it lands on 3.

Question 3Non-calculator4 marks

A spinner can land on $A$ , $B$ , $C$ or $D$ . P( $A$ ) $= 2x$ , P( $B$ ) $= x + 0.1$ , P( $C$ ) $= 0.3$ and P( $D$ ) $= x$ .

(a) Work out P( $B$ ).

(b) The spinner is spun 200 times. Work out an estimate for the number of times it lands on $B$ .

In past papers

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