A red spinner has four sides labelled 1, 2, 3, 4. When the spinner is spun, the score is the number on the side on which it lands. The random variable X denotes this score. The probability distribution table for X is given below. x | 1 | 2 | 3 | 4 P(X = x) | 0.28 | p | 2p | 3p A fair blue spinner and a fair green spinner each have four sides labelled 1, 2, 3, 4. All three spinners (red, blue and green) are spun at the same time.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [B1] Using sum of probabilities = 1 to form an equation. Accept 0.28 + p + 2p + 3p = 1, p = 0.12. Substitution of 0.12 into the expression scores B0.
2. [B1] Correct probability for 1 identified scenario, accept unsimplified, www.
3. [M1] Add values of 4 correct scenarios, may be implied by correct unsimplified expressions. No incorrect/repeated scenarios.
4. [A1] If A0 scored, SC B1 for 0.06 www.
5. [B1] Seen alone or as the denominator of a conditional probability fraction. Accept unsimplified.
6. [M1] Values of at least 5 identified correct scenarios added, accept unsimplified, condone incorrect scenarios in calculation.
7. [M1] 0.28×(0.25)²xx+0.24×(0.25)², or 0.0175 × x + 0.015 where x = 4, 5, 6, 7, or 8. Seen alone or as numerator/denominator of a conditional probability fraction.
8. [A1] 0.2980769... to at least 3SF.