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 has four colours on it. Priya spins the spinner $60$ times and records the colour it lands on.

$\begin{array}{l|cccc}\text{Colour} & \text{Red} & \text{Blue} & \text{Green} & \text{Yellow} \\ \hline \text{Frequency} & 24 & 15 & 9 & 12\end{array}$

(a) Use Priya's results to estimate the probability that the spinner lands on green.

(b) Priya spins the spinner a further $400$ times. Estimate the number of times it lands on red.
Level 3 · 4 marksTry it
2
Jamal rolls a dice $300$ times. He rolls a six $72$ times.

(a) Work out the relative frequency of rolling a six.

(b) Work out how many sixes Jamal would expect in $300$ rolls if the dice were fair.

(c) Do Jamal's results suggest that the dice is biased? Give a reason for your answer.
Level 3 · 4 marksTry it
3
In a computer game, Leo attempts a level $80$ times and completes it $28$ times.

(a) Use these results to estimate the probability that Leo completes the level on any one attempt.

(b) Leo attempts the level $250$ more times. Estimate the number of times he completes it.

(c) Explain why your answer to part (b) cannot be the actual number of times Leo completes the level.
Level 3 · 5 marksTry it