Jasmine throws two ordinary fair 6-sided dice at the same time and notes the numbers on the uppermost faces. The events A and B are defined as follows. A: The sum of the two numbers is less than 6. B: The difference between the two numbers is at most 2.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [B1] P(A) = 10/36
2. [B1] Accept P(A) = 10/36, 5/18, 0.278
3. [B1] P(B) = 24/36
4. [B1] and P(B) = 24/36, 2/3, 0.667.
5. [B1] P(A ∩ B) = 8/36
6. [M1] Their P(A) × their P(B) seen numerically, 0 < their P(A), P(B) ≤ 1.
7. [A1 FT] Multiplication evaluated correctly and compared with intersection that is not a product of multiplication, conclusion stated, notation P(A), P(B) and P(A ∩ B) used.
8. [M1] [P(B ∩ A') =] 16/36
9. [M1] or their P(B) – their P(A ∩ B) seen as numerator or denominator of conditional probability fraction.
10. [M1] [P(A') =] (1-10/36) = 26/36
11. [M1] or 1 – their P(A) seen as denominator of conditional probability fraction.
12. [A1] Final answer 16/26, 8/13
13. [A1] 0.6153846 to at least 3SF.
14. [M1] [Number of outcomes (B ∩ A') =] 16 seen as numerator or denominator of conditional probability fraction.
15. [M1] [Number of outcomes (A') =] 26 seen as denominator of conditional probability fraction.