GCSE · Basic probability

Relative frequency & expected outcomesExam-style questions

Estimating a probability from data — relative frequency is frequency divided by the number of trials — why more trials sharpen the estimate, how to test a dice or spinner for bias, and why the expected number is probability times trials.

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13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
A spinner is spun $50$ times. It lands on red $20$ times. Work out the relative frequency of red.
Level 1 · 1 markTry it
2
The probability that a biased coin lands heads is $0.6$ . The coin is flipped $200$ times. Estimate how many times it lands heads.
Level 1 · 1 markTry it
3
A dice is rolled $200$ times. It lands on $6$ on $44$ of the rolls.

(a) Work out the relative frequency of rolling a $6$ . (1 mark)

(b) The dice is rolled $500$ times. Estimate the number of times it lands on $6$ . (1 mark)

(c) Do you think the dice is fair? Give a reason for your answer. (1 mark)
Level 2 · 3 marksTry it
4
A spinner has four equal sections coloured red, blue, green and yellow.

The spinner is spun $80$ times. Here are the results.
Colour Red Blue Green Yellow
Frequency 28 20 12 20
(a) Work out the relative frequency of red. (1 mark)
(b) Is the spinner fair? Give a reason for your answer. (1 mark)
(c) The spinner is spun $400$ times. Estimate the number of times it will land on red. (1 mark)
Level 2 · 3 marksTry it
5
Sam drops a drawing pin $200$ times. It lands point-up $130$ times.

(a) Use Sam's results to estimate the probability that the pin lands point-up.

(b) Estimate the probability that the pin lands point-down.
Level 2 · 3 marksTry it

Colour	Red	Blue	Green	Yellow
Frequency	28	20	12	20

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