A-LevelMathematicsProbability and statistics9709/51 · May/June 2023 · Q78 Marks

A children's wildlife magazine is published every Monday. For the next 12 weeks it will include a model animal as a free gift. There are five different models: tiger, leopard, rhinoceros, elephant and buffalo, each with the same probability of being included in the magazine. Sahim buys one copy of the magazine every Monday.

(a)Find the probability that the first time that the free gift is an elephant is before the 6th Monday.[2]
(b)Find the probability that Sahim will get more than two leopards in the 12 magazines.[3]
(c)Find the probability that after 5 weeks Sahim has exactly one of each animal.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[M1] 1 - 0.8^r, r = 5, 6.
[A1]
[M1] One term ¹²Cₓ (p)ˣ (1-p)¹²⁻ˣ, 0 < p < 1, x ≠ 0, 1, 2.
[A1] Correct expression, accept unsimplified, no terms omitted, leading to final answer. Correct unsimplified expression or better.
[B1] 0.411 < p < 0.442 WWW.
[M1] (0.2)⁵ × s, s a positive integer. 1 may be implied.
[M1] t × 5! where 0 < t < 1.
[A1]

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