If $6 P(A) = 8 P(B) = 14 P(A \cap B) = 1$,then $P(A' \mid B) = $ . . . . . . .

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

Find $P(E | F)$ for a coin tossed three times,where $E:$ at most two tails,$F:$ at least one tail. (in $/7$)

Let $X$ and $Y$ be two events of a sample space such that $P(X)=\frac{1}{3}$,$P(X|Y)=\frac{1}{2}$ and $P(Y|X)=\frac{2}{5}$,then which of the following is true?

$A$ family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

The probabilities of Virat becoming the Man of the Match in the $1^{st}$,$2^{nd}$,and $3^{rd}$ matches of India in the World Cup $2015$ are $\frac{3}{7}$,$\frac{2}{7}$,and $\frac{1}{7}$ respectively. If Virat got the Man of the Match in exactly one match,what is the probability that he got it in the $3^{rd}$ match?