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In a made-up city, 40% of households have a car, 50% have a bicycle and 25% have both…

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

In a made-up city, $40\%$ of households have a car, $50\%$ have a bicycle and $25\%$ have both. Find the probability that a household has a bicycle, given that it has a car. Find the probability that a household has a car, given that it has a bicycle. Then find the probability that a household has neither.

Need a reminder? The key ideaShow

In a two-way table, $P(A \mid B)$ is the count of $A$ and $B$ divided by the count of $B$ : look only at the row or column of $B$ . In shares, $P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}$ .

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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