CAIE A-Level Mathematics 6.1.1 Poisson Probabilities

Practise rescaling a Poisson mean for a changed interval and evaluating exact, ranged or tail probabilities with e^−λ λ^r/r!, finite sums and complements.

Exam points

scale λ by the ratio of the requested interval, area or population to the stated one
substitute r into e^−λ λ^r/r! for an exact number of randomly occurring events
sum the required integer terms or subtract an unwanted lower tail from one

[Maximum number: 2]

The number, X, of books received at a charity shop has a constant mean of 5.1 per day.

Find the probability that exactly 10 books are received in a 3-day period.

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6.1.1—Poisson probabilities question 1