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 $P(A) =$

Two integers are selected at random from the set $\{1, 2, \dots, 11\}.$ Given that the sum of the selected numbers is even,what is the conditional probability that both numbers are even?

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 not mutually exclusive events. If $P(A) = \frac{4}{9}$ and $P(A \cap \bar{B}) = \frac{3}{7}$, then find $P\left(\frac{B}{A}\right)$.

Two events $A$ and $B$ are such that $P(A)=\frac{1}{4}$, $P(A|B)=\frac{1}{4}$ and $P(B|A)=\frac{1}{2}$. Consider the following statements:
$(I) P(\bar{A}|\bar{B})=\frac{3}{4}$
$(II) A$ and $B$ are mutually exclusive
$(III) P(A|B)+P(A|\bar{B})=1$
Then,

Two cards are drawn one by one from a pack of cards. The probability of getting the first card as an ace and the second as a coloured card is (without replacement).