For two events, $A$ and $B , P ( A ) = \frac { 1 } { 2 } , P ( B ) = \frac { 1 } { 3 }$, and $P ( A \cap B ) = \frac { 1 } { 4 }$. Find $P ( B \mid A )$.
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 12 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 1 } { 8 }$

Question

Quizplus · Accepted Answer

The probability of $B$ given $A$ is calculated using the formula $P(B|A) = \frac{P(A \cap B)}{P(A)}$. Substituting the given values, we get $P(B|A) = \frac{1/4}{1/2} = \frac{1}{2}$.

For Two Events AAA And B,P(A)=12,P(B)=13B , P ( A ) = \frac { 1 } { 2 } , P ( B ) = \frac { 1 } { 3 }B,P(A)=21​,P(B)=31​

For Two Events $A$ And $B , P ( A ) = \frac { 1 } { 2 } , P ( B ) = \frac { 1 } { 3 }$