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If $\mathrm{A}$ and $\mathrm{B}$ are independent, then
$P$ (exactly one of $A, B$ occurs)
$=\mathrm{P}(\mathrm{A}) \mathrm{P}\left(\mathrm{B}^{\prime}\right)+\mathrm{P}(\mathrm{B}) \mathrm{P}\left(\mathrm{A}^{\prime}\right)$
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$P$ (exactly one of $A, B$ occurs)
$=\mathrm{P}(\mathrm{A}) \mathrm{P}\left(\mathrm{B}^{\prime}\right)+\mathrm{P}(\mathrm{B}) \mathrm{P}\left(\mathrm{A}^{\prime}\right)$
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