A fair red spinner has edges numbered 1, 2, 2, 3. A fair blue spinner has edges numbered -3, -2, -1, -1. Each spinner is spun once and the number on the edge on which each spinner lands is noted. The random variable X denotes the sum of the resulting two numbers.

Mark scheme

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

1. B1 Table with correct X values and at least one probability 0 <p<1. Condone any additional X values if probability stated as 0. No repeated X values.
2. B1 3 correct probabilities linked with correct outcomes, may not be in table.
3. B1 2 further correct probabilities linked with correct outcomes, may not be in table No repeated X values.
4. SC if less than 3 correct probabilities seen, award SCB1 Sum of their probabilities, 0 < p <1, of 4,5 or 6 X values = 1 (condone summing to 1±0.01 or better).
5. X: -2, -1, 0, 1, 2
6. P(X): 1/16, 3/16, 5/16, 5/16, 2/16 (or decimal equivalents)
7. M1 Appropriate variance formula using (E(X))² value, accept unsimplified. FT their table with at least 3 different X values even if probabilities not summing to 1, 0 < p < 1. Condone 1 error providing all probabilities <1 and 0.252 used
8. A1 Condone 1.188 or 1.19 WWW
9. Var(X) = Σx²P(X=x) - (E(X))²
10. Σx²P(X=x) = (-2)²(1/16) + (-1)²(3/16) + (0)²(5/16) + (1)²(5/16) + (2)²(2/16) = (4+3+0+5+8)/16 = 20/16 = 1.25
11. Var(X) = 1.25 - (0.25)² = 1.25 - 0.0625 = 1.1875