For any two events $A$ and $B$,if $P(A) + P(B) - P(A \cap B) = P(A)$,then . . . . . . .

$A$ black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than $9,$ given that the black die resulted in a $5$.

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

Find $P(E | F)$ for a coin tossed three times,where $E: \text{head on third toss}$,$F: \text{heads on first two tosses}$.

Let $A, B, C$ be pairwise independent events with $P(C) > 0$ and $P(A \cap B \cap C) = 0$. Then $P(A' \cap B' | C) = $

$A$ college student has to appear for two examinations $A$ and $B$. The probabilities that the student passes in $A$ and $B$ are $\frac{2}{3}$ and $\frac{3}{4}$ respectively. If it is known that the student passes at least one among the two examinations,then the probability that the student will pass both the examinations is