If $P(A) = \frac{7}{13}$,$P(B) = \frac{9}{13}$ and $P(A \cap B) = \frac{4}{13}$,evaluate $P(A | B)$.

Bill and George go target shooting together. Both shoot at a target at the same time. Suppose Bill hits the target with probability $0.7$ whereas George,independently,hits the target with probability $0.4$. Given that exactly one shot hit the target,what is the probability that it was George's shot?

If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$,then $P(B/A) = $

Let $A$ and $B$ be two independent events such that $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{6}$. Then,which of the following is $TRUE$?

For any two events $A$ and $B$,if $P(A) + P(B) - P(A \cap B) = P(A)$,then . . . . . . .

Consider the experiment of throwing a die. If a multiple of $3$ comes up,throw the die again,and if any other number comes,toss a coin. Find the conditional probability of the event 'the coin shows a tail',given that 'at least one die shows a $3$'.