For independent events A and B,if P(A) = p,P( | vedclass

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(D) Given that $A$ and $B$ are independent events,we have $P(A \cap B) = P(A) \cdot P(B)$.Substituting the given values,$P(A \cap B) = p \cdot \frac{1

Vedclass · Accepted Answer

$\frac{1}{5}$

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(D) Given that $A$ and $B$ are independent events,we have $P(A \cap B) = P(A) \cdot P(B)$.Substituting the given values,$P(A \cap B) = p \cdot \frac{1}{2} = \frac{p}{2}$.We know the formula for the union of two events: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the known values: $\frac{3}{5} = p + \frac{1}{2} - \frac{p}{2}$.Simplifying the equation: $\frac{3}{5} - \frac{1}{2} = p - \frac{p}{2}$.$\frac{6 - 5}{10} = \frac{p}{2}$.$\frac{1}{10} = \frac{p}{2}$.Therefore,$p = \frac{2}{10} = \frac{1}{5}$.Thus,the correct option is $D$.

For independent events $A$ and $B$,if $P(A) = p$,$P(B) = \frac{1}{2}$,and $P(A \cup B) = \frac{3}{5}$,then find the value of $p$.

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