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For two events, P(A) = 0.4, P(B) = 0.25 and P(A ∩ B) = 0.1…

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

For two events, $P(A) = 0.4$ , $P(B) = 0.25$ and $P(A \cap B) = 0.1$ . Find the product $P(A) \times P(B)$ and decide whether the events are independent. Then find $P(A \cup B)$ and the probability of neither. Check that the probability of neither equals $P(\text{not } A) \times P(\text{not } B)$ .

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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