Q.If two events $A$ and $B$ are dependent, then the conditional probability of $P(B/A)$ is :

For independent events $P(A\cap B)=P(A)\cdot P(B)=\dfrac{3}{25}$.

Two events $A$ and $B$ are independent when the occurrence of one does not affect the probability of the other. For such events the multiplication rule simplifies to:

$P(A\cap B)=P(A)\times P(B).$

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For dependent events, $P(B/A)=\dfrac{P(A\cap B)}{P(A)}$.

The conditional probability of event $B$ occurring, given that event $A$ has already occurred, is defined as:

$P(B/A)=\frac{P(A\cap B)}{P(A)},\qquad P(A)\neq 0.$

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If one event's outcome has no effect on another, the events are independent.

When the outcome of one event does not influence the probability of another event, the two events are said to be independent; formally $P(A\cap B)=P(A)\,P(B)$.

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Because $A$ and $B$ are independent, $P(A\cap B)=P(A)P(B)=\dfrac{2}{5}\cdot\dfrac{1}{5}=\dfrac{2}{25}$.

Two events $A$ and $B$ are independent when the occurrence of one does not affect the probability of the other. For such events the multiplication rule simplifies to:

$P(A\cap B) = P(A)\cdot P(B).$ …