Let A and B be two independent events. If P(A | vedclass

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(A) Let $P(\overline{B}) = x$. Then $P(B) = 1 - x$.Since $A$ and $B$ are independent events,$P(A \cap B) = P(A)P(B) = \frac{1}{5}(1 - x)$.We know that

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(A) Let $P(\overline{B}) = x$. Then $P(B) = 1 - x$.Since $A$ and $B$ are independent events,$P(A \cap B) = P(A)P(B) = \frac{1}{5}(1 - x)$.We know that $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the given values: $\frac{7}{10} = \frac{1}{5} + (1 - x) - \frac{1}{5}(1 - x)$.$\frac{7}{10} = \frac{1}{5} + (1 - x)(1 - \frac{1}{5})$.$\frac{7}{10} - \frac{2}{10} = (1 - x)(\frac{4}{5})$.$\frac{5}{10} = (1 - x)(\frac{4}{5})$.$\frac{1}{2} = (1 - x)(\frac{4}{5})$.$1 - x = \frac{1}{2} 	imes \frac{5}{4} = \frac{5}{8}$.Since $P(\overline{B}) = x$,we have $x = 1 - \frac{5}{8} = \frac{3}{8}$.

Let $A$ and $B$ be two independent events. If $P(A) = \frac{1}{5}$ and $P(A \cup B) = \frac{7}{10}$,then what is the value of $P(\overline{B})$?

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