Birgitte has a six-sided dice. She suspects that the dice is biased so that the probability, p, that it will show a six on one throw is less than 1/6. She throws the dice 30 times and finds that it shows a six on exactly 2 throws.
Later, Birgitte carries out a similar test at the 5% significance level, using another 30 throws of the dice.

Q: What topic does this question test?

This question tests Probability and statistics in A-Level Mathematics (syllabus code 9709). It is worth 10 marks.

Q: Which exam paper is this question from?

This question appeared in the Cambridge A-Level Mathematics May/June 2025 examination, Paper 6 Variant 2 (9709_s25_qp_62.pdf).

Question

Birgitte has a six-sided dice. She suspects that the dice is biased so that the probability, p, that it will show a six on one throw is less than 1/6. She throws the dice 30 times and finds that it shows a six on exactly 2 throws.
Later, Birgitte carries out a similar test at the 5% significance level, using another 30 throws of the dice.

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