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?
