On any given day, Cooper either wears a blue jumper or he wears a green jumper or he does not wear a jumper. The probability that he wears a blue jumper is 0.6 and the probability that he wears a green jumper is 0.3. Whether Cooper wears a jumper of either colour, or does not wear a jumper, on any day is independent of his choice on any other day.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [M1] One term of the form 7Cx (p)x(1-p)7-x. 0<p<1,x≠0 or 7.
2. [A1] Correct un-simplified expression no terms omitted leading to the final answer.
3. [B1] 0.4198<p ≤ 0.42[0].
4. [M1] One term of the form 7Cx (p)x(1-p)7-x 0<p<1,x≠0 or 7.
5. [A1] Correct un-simplified expression, no more than 2 ‘middle' terms omitted leading to the final answer. Condone omission of final bracket '}'. If other brackets omitted, allow recovery if correct answer obtained.
6. [B1] 0.4198 < p < 0.42[0].
7. [B1] 15 and 13.5 seen, allowed un-simplified. May be seen in the standardisation formula. (σ= √13.5,3.674 <σ≤3.6742346 implies correct variance). Withhold mark if variance clearly identified as standard deviation, condone N (15,√13.5) (15,13.5) if standardisation formula correct or variance/standard deviation correctly stated as well.
8. [M1] Substituting their μ and σ into the ±standardising formula (any number for 21.5), allow σ² or √σ.
9. [M1] Use continuity correction 21.5 or 22.5 in standardisation formula.
10. [M1] Appropriate area Φ, from final process, must be a probability Note: correct final answer implies this M1.
11. [A1] AWRT 0.962.