If $A$ and $B$ are independent events with $P(A) = \frac{1}{3}$ and $P(B) = \frac{2}{7}$,then the value of $P\left(\frac{A}{B^C}\right)$ is

Statement $- I :$ If $A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/5$,then $P(A|B) = 1/2$.
Statement $- II : P(A|B) = P(A)$ if $A$ and $B$ are independent events.

Two cards are drawn randomly from a pack of $52$ playing cards one after the other with replacement. If $A$ is the event of drawing a face card in the first draw and $B$ is the event of drawing a club card in the second draw,then $P(\overline{B}|A) = $

If $A$ and $B$ are events such that $P(A | B) = P(B | A)$,then

Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that the youngest is a girl?

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 $P\left(\frac{B}{A}\right)$.