The numbers on the faces of a fair six-sided dice are 1, 2, 2, 3, 3, 3. The random variable X is the total score when the dice is rolled twice.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [B1] Table with correct X values and at least one correct probability associated with the correct X value. Values need not be in order, lines may not be drawn, may be vertical, X and P(X) may be omitted. Condone any additional X values if probability stated as 0.
2. [B1] Three other probabilities associated with correct x values, need not be in table, accept unsimplified.
3. [B1] Five correct probabilities linked with correct outcomes, may not be in table. Decimals correct to at least 3sf. SC B1 for five probabilities summing to 1 placed in a probability distribution table with the correct x values.
4. [M1] Accept unsimplified expression or sum of fractions seen. May be calculated in variance. FT their table with five probabilities summing to 0.999 < total < 1 (0 < p < 1).
5. [M1] 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. Note: If table is correct, then (824/36) or (206/9) or 22.89 or (196/9) or 21.78 or (14/3)² implies M1.
6. [A1] 10/9, 1.11[1], 1.1
7. [M1] their P(4)+their P(6) / their P(4)+P(5)+P(6) all probabilities (0 < p < 1). If sample space seen in any part of the question, then M1 their 19 / their 31
8. [A1] 0.613