$A$ bag contains $3$ white and $2$ red balls. If the first ball drawn is not replaced,what is the probability that the second ball is red?

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

$A$ 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

Two dice are thrown simultaneously. If $A$ is the event of getting the sum of the numbers on two dice as greater than or equal to $8$ and $B$ is the event of getting a number less than or equal to $3$ on at least one of the dice. Then,$P(B / A) = $

$E_1$ and $E_2$ are two independent events of a random experiment such that $P(E_1) = \frac{1}{2}$ and $P(E_1 \cup E_2) = \frac{2}{3}$. Match the items of List-$I$ with the items of List-$II$.

List-$I$	List-$II$
$A$. $P(E_2)$	$(i)$ $\frac{1}{2}$
$B$. $P(\frac{E_1}{E_2})$	$(ii)$ $\frac{5}{6}$
$C$. $P(\frac{\bar{E}_2}{E_1})$	$(iii)$ $\frac{1}{3}$
$D$. $P(\bar{E}_1 \cup \bar{E}_2)$	$(iv)$ $\frac{1}{6}$
	$(v)$ $\frac{2}{3}$

Find $P(E | F)$ for a coin tossed three times,where $E:$ at most two tails,$F:$ at least one tail. (in $/7$)