A factory produces chocolates. 30% of the chocolates are wrapped in gold foil, 25% are wrapped in red foil and the remainder are unwrapped. Indigo chooses 8 chocolates at random from the production line.

Mark scheme

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

1. [M1] One term ⁸Cₓ (p)ˣ (1-p)⁸⁻ˣ, 0 < p < 1, 0 < x < 8.
2. [A1] Correct expression, accept unsimplified, no terms omitted leading to final answer.
3. [B1] AWRT.
4. [M1] One term ⁸Cₓ (p)ˣ (1-p)⁸⁻ˣ, 0 < p < 1, 0 < x < 8.
5. [A1] Correct expression, accept unsimplified, condone omission of up to 3 'middle' terms, leading to final answer.
6. [B1] AWRT.
7. [M1] 1-0.75ⁿ, n = 6, 7.
8. [A1] 0.82202148... to at least 3SF.
9. [M1] Summing 6 or 7 terms – condone extra term 0.25×0.75⁶.
10. [A1]
11. [M1] Correct expression.
12. [A1]
13. [M1] a×0.3×b×c×0.45 0 < a, b, c < 1. a ≠ 0.3, 0.45 b, c ≠ 0.45. multiplied in that order, or correct.
14. [A1] 5 correct probabilities multiplied.
15. [M1] ax0.3×b×c×0.45 0 < a, b, c < 1. a ≠ 0.3, 0.45 b, c ≠ 0.45. 4 terms in this form seen added on their own or as a numerator.
16. [A1] All probabilities correct and attempt to sum the 4 scenarios.
17. [B1] [P(5th is first unwrapped) =] (0.55)⁴ (0.45)[=0.041178]
18. [M1] their P(2nd gold ∩ 5th is first unwrapped) / their P(5th is first unwrapped) Their probabilities must be clearly identified if incorrect.
19. [A1] 0.24793...
20. [M1] Either 0.25/0.55 or 0.3/0.55 or 0.25/0.45 or 0.3/0.45
21. [A1] Either 0.25/0.55, 0.3/0.55 or 0.25/0.45, 0.3/0.45
22. [B1] Both probs correct, can be unsimplified.
23. [M1] Multiplying their identified P(red given wrapped) by their identified P(gold given wrapped) or correct.
24. [A1]