Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

Vehicles arriving at a particular road junction from town A may turn left, turn right, or continue straight ahead. It has been observed over time that, among vehicles approaching this junction from town A, $55\%$ turn left, $15\%$ turn right and $30\%$ continue straight ahead. The direction taken by one vehicle at the junction is independent of the direction chosen by any other vehicle at the junction.
(i)[4]

Find the probability that, among the next three vehicles approaching the junction from town A, one goes straight on while the other two are either both turn left or both turn right.

(ii)[4]

Three vehicles approach the junction from town A. Given that all three drivers select the same direction at the junction, find the probability that they all go straight on.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct working for single-case probabilities such as $P(SLL)$ or $P(SRR)$

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