Given that the two numbers appearing on throwing two dice are different,find the probability of the event 'the sum of numbers on the dice is $4$.'

If two events $A$ and $B$ are such that $P(\overline{A}) = 0.3$,$P(B) = 0.4$,and $P(A \cap \overline{B}) = 0.5$,then $P(B | (A \cup \overline{B})) = $

In a hostel,$60 \%$ of the students read Hindi newspaper,$40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. $A$ student is selected at random. If she reads Hindi newspaper,find the probability that she reads English newspaper.

Let $E^{C}$ denote the complement of an event $E$. Let $E_{1}, E_{2}$ and $E_{3}$ be any pairwise independent events with $P(E_{1}) > 0$ and $P(E_{1} \cap E_{2} \cap E_{3}) = 0$. Then $P(E_{2}^{C} \cap E_{3}^{C} / E_{1})$ is equal to

Bill and George go target shooting together. Both shoot at a target at the same time. Suppose Bill hits the target with probability $0.7$ whereas George,independently,hits the target with probability $0.4$. Given that exactly one shot hit the target,what is the probability that it was George's shot?

$A$ bag contains $ 17 $ tickets numbered from $ 1 $ to $ 17 $. $A$ ticket is drawn at random,then another ticket is drawn without replacing the first one. The probability that both the tickets show even numbers is