A-LevelMathematicsProbability and statistics9709/61 · May/June 2024 · Q13 Marks

A bus station has exactly four entrances. In the morning the numbers of passengers arriving at these entrances during a 10-second period have the independent distributions Po(0.4), Po(0.1), Po(0.2) and Po(0.5). Find the probability that the total number of passengers arriving at the four entrances to the bus station during a randomly chosen 1-minute period in the morning is more than 3.

Find the probability that the total number of passengers arriving at the four entrances to the bus station during a randomly chosen 1-minute period in the morning is more than 3.[3]

Mark scheme

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

[B1] λ = 7.2
[M1] P(X> 3) = 1 - e-7.2(1+7.2+7.2^2/2!+7.2^3/3!) or 1 - e-7.2(1 + 7.2 + 25.92 + 62.21) or 1 - (0.0007466 + 0.005375 +0.01935 + 0.04644)
[A1] = 0.928 (3sf)

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source: A-Level Mathematics, May/June 2024 Paper 6 Variant 1, question 1.

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