A fair 6-sided die has the numbers 1, 2, 2, 3, 3, 3 on its faces. The die is rolled twice. The random variable X denotes the sum of the two numbers obtained.

Mark scheme

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

1. B1 Table with correct X values and at least one probability. Condone any additional X values if probability stated as 0.
2. B1 3 correct probabilities linked with correct outcomes. Accept 3 sf decimals.
3. B1 2 further correct probabilities linked with correct outcomes. Accept 3 sf decimals.
4. SC B1 for 5 probabilities (0 < p <1) that sum to 1 with less than 3 correct probabilities.
5. M1 Accept unsimplified expression. May be calculated in variance. FT their table with 4 or more probabilities summing to 0.999 < total < 1 (0 <p<1).
6. M1 Appropriate variance formula using their (E(X))² value. FT their table with 3 or more probabilities (0 <p<1) which need not sum to 1 and the calculation in bold (or less simplified) seen.
7. A1 Answers for E(X) and Var(X) must be identified. E(X) may be identified by correct use in Variance. Condone E, V, μ, σ² etc. If M0 earned SC B1 for identified correct final answers.