A fair red spinner has 4 sides, numbered 1, 2, 3, 4. A fair blue spinner has 3 sides, numbered 1, 2, 3. 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 2018). The mark or mark type is shown in brackets.

1. [B1] -2, -1, 0, 1, 2, 3 seen as top line of a pdf table with at least 1 probability OR attempting to evaluate P(-2), P(−1), P(0), P(1), P(2), P(3) (condone additional values with p=0 stated)
2. [B1] At least 4 probs correct (need not be in table)
3. [B1] All probs correct in a table
4. [M1] Unsimplified expression for mean using their pdf table (or correct) with at least 2 non-zero values (may be seen in variance). Numerator terms may be implied by values.
5. [M1] Unsimplified expression for variance using their pdf table (or correct) with at least 2 non-zero values and their E(X). Numerator terms may be implied by values. If –k² is seen for (−k)², the method must be confirmed by seeing value used correctly
6. [A1] Correct final answer
7. [B1ft] If Binomial distribution used 0/3 P(X non-zero) ft from their pdf table, Σp=1 oe
8. [M1] Their P(X = 1)/their P(X non-zero) from their pdf table oe
9. [A1] Correct final answer www