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A made-up building has two door sensors that work 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 building has two door sensors that work independently. When someone walks in, the first sensor reacts with probability $0.95$ and the second with probability $0.85$ . Find the probability that both react, the probability that at least one reacts, and the probability that exactly one reacts. Give four decimal places.

Need a reminder? The key ideaShow

Events are independent when one does not change the chance of the other. Then $P(A \cap B) = P(A) \times P(B)$ , and $P(\text{at least one}) = 1 - P(\text{none})$ .

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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