In a group of students, the numbers of boys and girls studying Art, Music and Drama are given in the following table. Each of these 160 students is studying exactly one of these subjects. Art Music Drama Boys 24 40 32 Girls 15 12 37

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

1. [B1] 52/160 = 13/40, 0.325; oe
2. [M1] Use of P(B) × P(M) = P(B∩M), appropriate probabilities used
3. [A1] Numerical comparison and conclusion stated
4. [M1] Method 1: P(not Music/girl) = P(not Music and girl)/P(girl); Appropriate probabilities in a fraction
5. [A1] Method 1: = 27/64; Correct answer www implies method
6. [M1] Method 2: Direct from table; 27/a or b/64, a ≠ 160
7. [A1] Method 2: = 27/64; Correct answer www implies method
8. [M1] Method 1: One scenario identified with 3 probs multiplied
9. [A1] Method 1: One scenario correct (ignore multiplying factor)
10. [B1] Method 1: Both multiplying factors correct
11. [M1] Method 1: Both cases attempted and added (multiplying factor not required), accept unsimplified
12. [A1] Method 1: P = 0.201; Correct answer, oe
13. [M1] Method 2: One scenario identified with 2 or 3 combination multiplied
14. [A1] Method 2: One scenario correct
15. [B1] Method 2: Denominator correct
16. [M1] Method 2: Both scenarios attempted, and added, seen as a numerator of a fraction
17. [A1] Method 2: Correct answer, oe