It is given that $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$. Then $P(B) = $?

An urn $A$ contains $3$ white and $5$ black balls. Another urn $B$ contains $6$ white and $8$ black balls. $A$ ball is picked from $A$ at random and then transferred to $B$. Then,a ball is picked at random from $B$. The probability that it is a white ball is

If $4\,P(A) = 6\,P(B) = 10\,P(A \cap B) = 1$,then $P\left( \frac{B}{A} \right) = \dots$

$A$ parent has two children. If at least one of them is a boy,then the probability that the other is also a boy is:

Compute $P(A | B),$ if $P(B)=0.5$ and $P(A \cap B)=0.32$.

$A$ box contains $10$ mangoes,out of which $4$ are spoiled. $2$ mangoes are taken together at random. If one of them is found to be good,then the probability that the other is also good is: