A-LevelMathematicsProbability and statistics9709/51 · Oct/Nov 2023 · Q27 Marks
Hazeem repeatedly throws two ordinary fair 6-sided dice at the same time. On each occasion, the score is the sum of the two numbers that she obtains.
- (a)Find the probability that it takes exactly 5 throws of the two dice for Hazeem to obtain a score of 8 or more.[2]
- (b)Find the probability that it takes no more than 4 throws of the two dice for Hazeem to obtain a score of 8 or more.[2]
- (c)For 8 randomly chosen throws of the two dice, find the probability that Hazeem obtains a score of 8 or more on fewer than 3 occasions.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [M1] (1-p)ʳ⁻¹xp, 0<p<1
- [A1] 0.0482454... to at least 3SF.
- [M1] 1-bʳ, b = their (1–p) in 2(a) or correct; r = 4, 5.
- [A1] 0.884211... to at least 3SF.
- [M1] p + p(1-p) + p(1 –p)² + p(1 –p)³ [+p(1-p)⁴)] FT from 2(a) or correct.
- [A1] 0.884211... to at least 3SF.
- [M1] One term ⁸Cₓ(q)ˣ(1-q)⁸⁻ˣ, 0<q<1, x≠0,8.
- [A1 FT] Correct expression, accept unsimplified, no terms omitted leading to final answer. FT only with unsimplified expression.
- [B1] 0.2815 ≤ q < 0.282
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