$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B | A)$ if $A \cap B = \phi$.

If $P(A)=0.25, P(B)=0.55$ and $P(A \cup B)=0.65$,then $P(B' \mid A) =$ . . . . . . .

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each,then the conditional probability that all children are girls given that at least two are girls is

$A$ box contains $3$ white and $2$ red balls. One ball is drawn at random,and then a second ball is drawn without replacement. What is the probability that the second ball is red?

If the events $A$ and $B$ are mutually exclusive,then $P\left( \frac{A}{B} \right) = $

If $P(AB) = P(A)P(B)$,$P(A/B) = 1/4$,and $P(B/A) = 1/3$,then which of the following is true?