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Two made-up swimming pools run a swimming test…

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

Two made-up swimming pools run a swimming test. At pool R, $30$ of $60$ beginners and $38$ of $40$ experienced swimmers pass. At pool S, $9$ of $20$ beginners and $72$ of $80$ experienced swimmers pass. Find the pass rate of beginners and of experienced swimmers at pool R, and the overall pass rate at each pool, as percentages.

Need a reminder? The key ideaShow

Simpson's paradox: a comparison holds inside every group but reverses when the groups are combined. An overall rate is a weighted average of the group rates: add the passes of all the groups, then divide by the total number in all the groups.

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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