$A$ box contains $3$ white and $2$ red balls. $A$ ball is drawn and another ball is drawn without replacing the first ball. What is the probability that the second ball is red?

If $A$ and $B$ are two events such that $P(A | B) = 0.6$,$P(B | A) = 0.3$,and $P(A) = 0.1$,then $P(\bar{A} \cap \bar{B})$ equals:

Two dice $A$ and $B$ are rolled. If it is known that the number on $B$ is $5$,then the probability that the sum of the numbers on the two dice will be greater than $9$ is

$A$ and $B$ are independent events of a random experiment if and only if

If $A$ and $B$ are two events such that $P(A \cap B) = 0.1$,and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12x^2 - 7x + 1 = 0$,then the value of $\frac{P(\overline{A} \cup \overline{B})}{P(\overline{A} \cap \overline{B})}$ is:

$A$ 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