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A made-up minibus company has 20 seats on each trip…

Contributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A made-up minibus company has $20$ seats on each trip. Some people who book do not turn up, so it takes $22$ bookings. Each person who books turns up with probability $0.9$ , independently of the others. Find the probability that $21$ people turn up, and the probability that all $22$ turn up. Then find the probability that more people turn up than there are seats. Find the expected number who turn up. Give four decimal places.

Need a reminder? The key ideaShow

For $X \sim B(n, p)$ :

\displaystyle P(X = k) = \binom{n}{k}p^k(1 - p)^{n-k}, \qquad \mu = np, \qquad \sigma = \sqrt{np(1 - p)}.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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