Let $A$ and $B$ be two events with $P(A^{C}) = 0.3$, $P(B) = 0.4$, and $P(A \cap B^{C}) = 0.5$. Then $P(B \mid A \cup B^{C})$ is equal to

$A$ 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

If $A$ and $B$ are two non-mutually exclusive events such that $P(A \mid B) = P(B \mid A)$,then

Suppose that $E_1$ and $E_2$ are two events of a random experiment such that $P(E_1) = \frac{1}{4}$,$P(E_2 / E_1) = \frac{1}{2}$ and $P(E_1 / E_2) = \frac{1}{4}$. Observe the lists given below. The correct matching of List-$I$ with List-$II$ is:

List-$I$	List-$II$
$(A)$ $P(E_2)$	$(i)$ $1/4$
$(B)$ $P(E_1 \cup E_2)$	$(ii)$ $5/8$
$(C)$ $P(\bar{E}_1 / \bar{E}_2)$	$(iii)$ $1/8$
$(D)$ $P(E_1 / \bar{E}_2)$	$(iv)$ $1/2$
	$(v)$ $3/8$
	$(vi)$ $3/4$

Two persons $P$ and $Q$ are considering applying for a job. The probability that $P$ applies for the job is $1/4$,the probability that $P$ applies for the job given that $Q$ applies for the job is $1/2$,and the probability that $Q$ applies for the job given that $P$ applies for the job is $1/3$. Then the probability that $P$ does not apply for the job given that $Q$ does not apply for the job is

Ten cards numbered $1$ to $10$ are placed in a box,mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than $3,$ what is the probability that it is an even number (in $/7$)?