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.

Start practising Read the lesson

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 company tests a sample of $500$ of its light bulbs. $12$ of them fail within a year.

(a) Use this sample to estimate the probability that a bulb fails within a year.

(b) The company sells $25\,000$ bulbs. Every bulb that fails within a year is replaced, at a cost of £ $3.50$ to the company. Estimate the total replacement cost.

(c) The company then tests a second sample of $1500$ bulbs, of which $27$ fail within a year. Use both samples to give a better estimate of the probability that a bulb fails within a year.

(d) Explain why your answer to part (c) is a better estimate than your answer to part (a).
Level 5 · 8 marksTry it