If $80 \%$ of flights depart on time, $70 \%$ of flights arrive on time and $65 \%$ of flights depart on time and arrive on time, then the probability that a flight that has just departed on time will arrive on time is

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

If $A$ and $B$ are events such that $P(A) > 0$ and $P(B) \neq 1$,then $P(A \mid B^{\prime}) = $ . . . . . . .

Two cards are drawn from a pack of $52$ playing cards one after the other. If $p_1$ is the probability of getting a queen in the first draw and a diamond card in the second draw when the first card drawn is replaced, and $p_2$ is the probability of the same event when the first card drawn is not replaced, then $\frac{p_1}{p_2} = $

$A$ coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which the first throw is a head,then $P(E|F) = $

If $A$ and $B$ are two events such that $P(A \cup B) = P(A \cap B)$,then the true relation is