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

If two unbiased dice are rolled simultaneously until a sum of the numbers appearing on these dice is either $7$ or $11$, then the probability that $7$ comes before $11$ is:

If $A$ and $B$ are independent events such that $P(A \cap B') = \frac{3}{25}$ and $P(A' \cap B) = \frac{8}{25}$,then $P(A) =$

If $P(A) = \frac{3}{10}$,$P(B) = \frac{3}{5}$,and $P(A \cup B) = \frac{3}{5}$,then find the value of $P(A|B) \times P(B|A)$.

If $C$ and $D$ are two events such that $P(D) \neq 0$,then which of the following statements is correct?

If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A | B).$