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A made-up factory makes phone cases, and each case is faulty with probability 0.05, independently…

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

A made-up factory makes phone cases, and each case is faulty with probability $0.05$ , independently. A box holds $12$ cases. Find the probability that no case in the box is faulty, the probability that exactly one is faulty, and the mean number of faulty cases per box. Give probabilities to 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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