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.

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

1. [B1] H₀: P(correct) = 1/6 H₁: P(correct) > 1/6 Allow p = 1/6 Allow p > 1/6
2. [M1] 1 - (¹⁵C₄ × (⁵/₆)¹¹ × (¹/₆)⁴ + ¹⁵C₃ × (⁵/₆)¹² × (¹/₆)³ + ¹⁵C₂ × (⁵/₆)¹³ × (¹/₆)² + ¹⁵ × (⁵/₆)¹⁴ × (¹/₆)¹ + (⁵/₆)¹⁵) Expression must be seen Allow one end error
3. [A1] 0.0898 or 0.0897 (3 sf) SC if M0 scored allow SCB1 for 0.0898 or 0.0897
4. [M1] 0.0898 < 0.1 Valid comparison For valid comparison with 0.9 (0.9102 > 0.9 seen the previous M1 and A1 can be recovered
5. [FTA1] [Reject H₀] There is evidence (at the 10% level) that Arvind can predict scores Not definite, e.g. not 'He can predict' or 'Claim true' In context and no contradictions