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A made-up survey of 150 cyclists records age and helmet use…

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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 survey of $150$ cyclists records age and helmet use. Of the $60$ cyclists under $16$ years old, $45$ wear a helmet. Of the $90$ cyclists aged $16$ or over, $54$ wear a helmet. Find the probability that a cyclist wears a helmet, given that the cyclist is under $16$ . Do the same for a cyclist aged $16$ or over. Then find the probability that a cyclist is under $16$ , given that the cyclist wears a helmet. Give four decimal places.

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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