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(D) Given that $A$ and $B$ are independent events. $P(A^{\prime}) = 0.75$,so $P(A) = 1 - P(A^{\prime}) = 1 - 0.75 = 0.25$. We know that for any two ev

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$\frac{8}{15}$

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(D) Given that $A$ and $B$ are independent events. $P(A^{\prime}) = 0.75$,so $P(A) = 1 - P(A^{\prime}) = 1 - 0.75 = 0.25$. We know that for any two events $A$ and $B$,$P(A \cup B) = P(A) + P(B) - P(A \cap B)$. Since $A$ and $B$ are independent,$P(A \cap B) = P(A) \cdot P(B)$. Substituting the given values: $0.65 = 0.25 + p - (0.25 \cdot p)$ $0.65 - 0.25 = p(1 - 0.25)$ $0.40 = 0.75p$ $p = \frac{0.40}{0.75} = \frac{40}{75} = \frac{8}{15}$.

If $A$ and $B$ are two independent events such that $P(A^{\prime}) = 0.75$,$P(A \cup B) = 0.65$ and $P(B) = p$,then the value of $p$ is

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