At a large college, all students who study Science also study exactly one of Art or Drama or Music. 20% of these students study Art, 45% study Drama and 35% study Music.

Mark scheme

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

1. [M1] 1-(0.55)³ [Might also be seen as 1 – ³C₀(0.55)³[(0.45)⁰].]
2. [A1] = 0.834, 6669/8000 AWRT.
3. [M1] ³C₁(0.45)(0.55)² + ³C₂(0.45)²(0.55) + (0.45)³[0.55]⁰
4. [A1] = 0.834, 6669/8000 AWRT.
5. [M1] One term of the form ¹⁰Cₓ (p)ˣ(1-p)¹⁰⁻ˣ, 0<p<1,x ≠ 0 or 10.
6. [A1] [P(8, 9, 10) =] ¹⁰C₈ 0.55⁸ 0.45² + ¹⁰C₉ 0.55⁹ 0.45¹ + 0.55¹⁰ [= 0.0763026 +0.0207241 + 0.00253295]. Correct un-simplified expression.
7. [B1] = 0.0996 (0.09955<p ≤ 0.0996.)
8. [M1] One term of the form ¹⁰Cₓ (p)ˣ(1-p)¹⁰⁻ˣ, 0 < p <1,x ≠ 0 or 10.
9. [A1] [1 - P(0,1,2,3,4,5,6,7)] 1-(0.45¹⁰ + ¹⁰C₁ 0.55 0.45⁹ + ... + ¹⁰C₇ 0.55⁷ 0.45³). Correct un-simplified expression. Condone omission of up to 5 of the 6 middle terms. Condone omission of last bracket only. If both brackets omitted in un-simplified expression, allow recovery for final stated calculation of 1 - 0.90044... or better.
10. [B1] = 0.0996 (0.09955 < p < 0.0996.)