Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

A survey is carried out to discover how many photos people capture on a one-week holiday and how often they look back at earlier photos. For a randomly chosen person, the probability of taking fewer than $100$ photos is $x$. The probability that these people view past photos at least $3$ times is $0.76$. For those who take at least $100$ photos, the probability that they view past photos fewer than $3$ times is $0.90$. This information is shown in the tree diagram. The probability that a randomly chosen person views past photos fewer than $3$ times is $0.801$.
(i)[3]

Find the value of $x$.

(ii)[4]

Given that a person views past photos at least $3$ times, find the probability that this person takes at least $100$ photos.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Equation correctly uses the sum of the probabilities of the two 2-factor cases and sets it equal to $0.801$

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