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Trying to confirm my solution on this problem:

$46\%$ patients received treatment $x$ ($x$ can be $x_1$ or $x_2$). Out of these, $20.8\%$ received $x_1$ and $27.7\%$ received $x_2$. Note that it is possible for the same patient to receive both $x_1$ and $x_2$.

How many patients only received $x_1$?


My solution

If we add $20.8+27.7=48.5$, we overcount those that received both treatments, because those are counted in both $20.8$ and $27.7$. The quantity $48.5-46=2.5\%$ is then the number of patients that received both treatments.

If $2.5\%$ received both and this is counted by both $20.8\%$ and $27.7\%$, then $20.8-2.5=18.3\%$ is the number that only received $x_1$.

Is this correct?

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    $\begingroup$ yes. that is the solution. $\endgroup$ Sep 12, 2015 at 9:36

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