If A and B are events of a random experiment | vedclass

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(C) Given,$P(\bar{A} \cup \bar{B}) = P(\overline{A \cap B}) = \frac{7}{10}$.Since $P(A \cap B) + P(\overline{A \cap B}) = 1$,we have:$P(A \cap B) = 1

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$\frac{7}{10}$

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(C) Given,$P(\bar{A} \cup \bar{B}) = P(\overline{A \cap B}) = \frac{7}{10}$.Since $P(A \cap B) + P(\overline{A \cap B}) = 1$,we have:$P(A \cap B) = 1 - \frac{7}{10} = \frac{3}{10}$.Also,the formula for the union of two events is:$P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the given values:$\frac{4}{5} = P(A) + \frac{2}{5} - \frac{3}{10}$.$P(A) = \frac{4}{5} - \frac{2}{5} + \frac{3}{10}$.$P(A) = \frac{2}{5} + \frac{3}{10} = \frac{4+3}{10} = \frac{7}{10}$.

If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$,$P(\bar{A} \cup \bar{B}) = \frac{7}{10}$,and $P(B) = \frac{2}{5}$,then $P(A)$ equals

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