A fair red spinner has four sides, numbered 1, 2, 3, 3. A fair blue spinner has three sides, numbered −1, 0, 2. When a spinner is spun, the score is the number on the side on which it lands. The spinners are spun at the same time. The random variable X denotes the score on the red spinner minus the score on the blue spinner.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

1. [B1] Table with correct values of x, at least 1 probability, all probabilities < 1
2. [B1] 2 probabilities correct, may not be in table
3. [B1] 2 more probabilities correct, may not be in table
4. [B1] All correct, values in table SC1 No more than 1 correct probability and at least 5 probabilities summing to 1 in table
5. [M1] May be implied by use in variance. Allow unsimplified expression E(X) = (-1*1 + 0*1 + 1*3 + 2*2 + 3*3 + 4*2) / 12 = (-1+0+3+4+9+8)/12 = 23/12
6. [M1] Appropriate variance formula using their E(X)² Var(X) = E(X²) - (E(X))² = ((-1)²*1 + 0²*1 + 1²*3 + 2²*2 + 3²*3 + 4²*2)/12 - (23/12)² = (1+0+3+8+27+32)/12 - (23/12)² = 71/12 - (23/12)²
7. [A1] CAO 2.24 or 323/144 or 2 35/144