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Determine the probability that, among $350$ randomly chosen people, at least $47$ will have a Monday birthday for their next birthday.
Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
For a person chosen at random, the weekday of their next birthday is equally likely to be any day of the week, and it is independent of every other person’s birthday.
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This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Without simplifying, $np = 350 \times \frac{1}{7}$ and $npq = 350 \times \frac{1}{7} \times \frac{6}{7}$ are correct” …
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