$A$ box contains $3$ white and $2$ red balls. $A$ ball is drawn and another ball is drawn without replacing the first ball. What is the probability that the second ball is red?

$A$ fair die is rolled. Consider events $E=\{1,3,5\}, F=\{2,3\}$ and $G=\{2,3,4,5\}$. Find $P(E | F)$ and $P(F | E)$.

If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P(B \mid A) = 1$,then . . . . . . .

Consider the experiment of tossing a coin. If the coin shows head,toss it again but if it shows tail,then throw a die. Find the conditional probability of the event that 'the die shows a number greater than $4$' given that 'there is at least one tail'.

Find $P(E | F)$ when two coins are tossed once,where $E$ is the event that no tail appears and $F$ is the event that no head appears.

$A$ family has $3$ children. The probability that all the three children are girls,given that at least one of them is a girl is: