At a college, the students choose exactly one of tennis, hockey or netball to play. The table shows the numbers of students in Year 1 and Year 2 at the college playing each of these sports. Tennis Hockey Netball Year 1 16 22 12 Year 2 24 18 28 One student is chosen at random from the 120 students. Events X and N are defined as follows: X: the student is in Year 1 N: the student plays netball.

Mark scheme

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

1. [B1] 0.3, 3/10, 30% OE.
2. [B1] 0.24, 6/25 OE.
3. [B1] P(N),P(X)andP(N∩X)or P(N and X) notation seen and equated to the values for P(N),P(X)and P(N∩X) or P(N and X ).
4. Calculation stated and evaluated.
5. Not independent clearly stated.
6. 5/12 ≠ 12/120 does not need to be stated.
7. All values OE.
8. Condone consistent use of A, B etc.
9. If values for P(N), P(X) stated, accept P(N)×P(X) = 5/36
10. [M1] One term of form ⁸Cₓ (p)ˣ(1-p)⁸⁻ˣ. With 0<p<1, x≠0 or 8.
11. [A1] Correct unsimplified expression, no terms omitted leading to final answer.
12. [B1] 0.8945 < p < 0.895.