A game is played with an ordinary fair 6-sided die. A player throws the die once. If the result is 2, 3, 4 or 5, that result is the player's score and the player does not throw the die again. If the result is 1 or 6, the player throws the die a second time and the player's score is the sum of the two numbers from the two throws.

Mark scheme

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

1. [B1] 1st throw fully correct with probabilities and outcomes identified. (Probabilities all 1/6 and outcomes (1,2,3,4,5,6) on branches).
2. [B1] 2nd throw fully correct with probabilities and outcomes identified. (Probabilities all (all) 1/6 and outcomes (1,2,3,4,5,6) on branches).
3. [B1] P(5) or P(7) identified and correct unsimplified, accept if supported by correct scenarios shown or from tree diagram .
4. [M1] Adding only the values from 5 correct scenarios.
5. [A1] Scenarios identified (may be on tree diagram in 5(a)), all probabilities seen, WWW AG.
6. [M1] Both identified and evaluated, consistent with their tree diagram or correct.
7. [A1] P(A) × P(B) seen and evaluated, all notation present and correct. Correct conclusion WWW.
8. [B1] their 6/36 oe as numerator of a fraction.
9. [M1] their 6/36 / their (1 - 1/3) or correct seen, consistent with their tree diagram.
10. [A1] 1/4, 0.25