A fair coin and an ordinary fair six-sided dice are thrown at the same time. The random variable X is defined as follows. • If the coin shows a tail, X is twice the score on the dice. • If the coin shows a head, X is the score on the dice if the score is even and X is 0 otherwise.

Mark scheme

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

1. [B1] Table with correct x values and at least 2 correct probabilities. Condone any additional x values if probability stated as 0.
2. [B1] Four more probabilities correctly linked to the correct x value, need not be in table, accept unsimplified.
3. [B1] 7 correct probabilities linked with correct outcomes, may not be in table. Decimals correct to at least 3 SF. SC B1 7 or more probabilities summing to 1 placed in a probability distribution table.
4. [M1] Accept unsimplified expression. May be calculated in variance. Accept 2/3 + 2/3 + 5/3 + 1 + 25/12 + 1 OE for the M mark FT their table with 7 or 8 probabilities summing to 0.999 < total < 1 (0 < p < 1). FT acceptable at the bold partially evaluated stage.
5. [M1] Appropriate variance formula using their (E(X))² value. FT their table with 6 or more probabilities. (0 < p < 1) which need not sum to 1 or with an expression no more evaluated than shown. FT acceptable at the bold partially evaluated stage with their probabilities.
6. [A1] CAO Accept 59/4. If either or both M marks not awarded, SC B1 for correct answer WWW