A fair red spinner has 4 sides, numbered 1, 2, 3, 4. A fair blue spinner has 4 sides, numbered 0, 1, 2, 3. When a spinner is spun, the score is the number on the side on which it lands. The two spinners are spun at the same time. The random variable X denotes the higher of the two scores obtained. If the two scores are equal, then the value of X is 0.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [B1] Table with correct x values and one correct probability.
2. [B1] 2 more probabilities correct linked to the correct x value, need not be in table, accept un-simplified.
3. [B1] 5 correct probabilities linked with correct outcomes. SCB1 5 non-zero probabilities (not all 1/5) summing to 1 placed in a probability distribution table with correct x values if only one of the first two B marks are scored.
4. [M1FT] Accept un-simplified or bold expression with probabilities (0 < p < 1) that add to 1. May be calculated in variance. FT their table with 4 or 5 probabilities adding to 1.
5. [M1FT] Appropriate variance formula using their (E(X))² value. FT their table with 4 or more probabilities (0 < p < 1) which need not sum to 1 or with an expression no more evaluated than shown.
6. [A1] Accept 1.984375 to 3 or more SF. SCB1 for 1.98 if M0 M1 scored.
7. [M1] 1-(3/4)ⁿ with n = 6, 7, 8.
8. [A1] = 0.8665 to 4SF.