Arvind uses an ordinary fair 6-sided die to play a game. He believes he has a system to predict the score when the die is thrown. Before each throw of the die, he writes down what he thinks the score will be. He claims that he can write the correct score more often than he would if he were just guessing.
His friend Laxmi tests his claim by asking him to write down the score before each of 15 throws of the die. Arvind writes the correct score on exactly 5 out of 15 throws.

Q: What topic does this question test?

This question tests Probability and statistics in A-Level Mathematics (syllabus code 9709). It is worth 5 marks.

Q: Which exam paper is this question from?

This question appeared in the Cambridge A-Level Mathematics May/June 2022 examination, Paper 6 Variant 1 (9709_s22_qp_61.pdf).

Question

Arvind uses an ordinary fair 6-sided die to play a game. He believes he has a system to predict the score when the die is thrown. Before each throw of the die, he writes down what he thinks the score will be. He claims that he can write the correct score more often than he would if he were just guessing.
His friend Laxmi tests his claim by asking him to write down the score before each of 15 throws of the die. Arvind writes the correct score on exactly 5 out of 15 throws.

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