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If $\mathrm{P}(\mathrm{A})=\frac{2}{5}, \mathrm{P}(\mathrm{B})=\frac{1}{4}$ and $\mathrm{P}(\mathrm{AUB})=\frac{1}{2}$, then $\mathrm{P}\left(\mathrm{A}^{\prime} \cup \mathrm{B}^{\prime}\right)=$
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Verified Answer
The correct answer is:
$\frac{17}{20}$
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$P(A \cap B)=\frac{3}{20}$
$P(A \cap B)+P(\overline{A \cap B})=1$
$P(\overline{A \cap B})=\frac{17}{20}$
$P\left(A^{\prime} \cup B^{\prime}\right)=\frac{17}{20}$
$P(A \cap B)=\frac{3}{20}$
$P(A \cap B)+P(\overline{A \cap B})=1$
$P(\overline{A \cap B})=\frac{17}{20}$
$P\left(A^{\prime} \cup B^{\prime}\right)=\frac{17}{20}$
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