$A$ 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

If $A$ and $B$ are two events such that $P(B) \neq 0$ and $P(B) \neq 1$,then $P(\bar{A} \mid \bar{B})$ is equal to:

Let $A, B$ and $C$ be three events,which are pairwise independent and $\bar{E}$ denotes the complement of an event $E$. If $P(A \cap B \cap C) = 0$ and $P(C) > 0$,then $P[(\bar{A} \cap \bar{B})|C]$ is equal to

For two events $A$ and $B$,a true statement among the following is

Consider the experiment of throwing a die. If a multiple of $3$ comes up,throw the die again,and if any other number comes,toss a coin. Find the conditional probability of the event 'the coin shows a tail',given that 'at least one die shows a $3$'.

$A$ and $B$ are two groups of books. Group $A$ consists of $8$ science and $5$ engineering books,and group $B$ consists of $6$ science and $7$ engineering books. When an unbiased die is rolled,if $2$ or $5$ turns up,a book is selected at random from group $A$. Otherwise,a book is selected at random from group $B$. The probability of selecting a science book is