If $\mathrm{P}(\mathrm{A})=\frac{2}{5}, \mathrm{P}(\mathrm{B})=\frac{1}{4}$ and…

If $\mathrm{P}(\mathrm{A})=\frac{2}{5}, \mathrm{P}(\mathrm{B})=\frac{1}{4}$ and $\mathrm{P}(\mathrm{AUB})=\frac{1}{2}$, then $\mathrm{P}\left(\mathrm{A}^{\prime} \cup \mathrm{B}^{\prime}\right)=$
  1. $\frac{1}{2}$
  2. $\frac{1}{4}$
  3. $\frac{3}{20}$
  4. $\frac{17}{20}$

Solution

$P(A \cup B)=P(A)+P(B)-P(A \cap B)$ $P(A \cap B)=\frac{3}{20}$ $P(A \cap B)+P(\overline{A \cap B})=1$ $P(\overline{A \cap B})=\frac{17}{20}$ $P\left(A^{\prime} \cup B^{\prime}\right)=\frac{17}{20}$

Asked in: MHT CET 2020 (14 Oct Shift 1)

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