Salah decides to attempt the crossword puzzle in his newspaper each day. The probability that he will complete the puzzle on any given day is 0.65, independent of other days.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [B1] AWRT
2. [M1] (0.35)³ ×(0.65)² × k, where k is an integer. 1 ≤ k ≤ 5 no + or -
3. [A1]
4. [M1] One term 7Cx(p)x(1-p)7-x, 0<p<1, 0<x<7.
5. [A1] Correct expression, accept unsimplified, no terms omitted leading to final answer
6. [B1] AWRT
7. (M1) One term 7Cx(p)x(1-p)7-x, 0<p<1, 0<x<7.
8. (A1) Correct expression, accept unsimplified, no terms omitted leading to final answer.
9. (B1) AWRT
10. [B1] 54.6 and 19.11 seen, allow unsimplified. May be seen in the standardisation formula ([σ = ] 4.371 or (7√39)/10 implies correct variance). Incorrect notation is penalised, but condone use of values in standardisation formula.
11. [M1] Substituting their μ and their positive σ into the ±standardising formula (any number), not their σ², or √their σ.
12. [M1] Use continuity correction 49.5 or 50.5 in their standardisation formula. Note: ±4.1/√19.11 or ±4.1/4.371 seen gains M2 BOD.
13. [M1] Appropriate area Φ, from final process, must be a probability.
14. [A1] 0.8255 < p ≤ 0.826