$A$ box contains $b$ blue balls and $r$ red balls. $A$ ball is drawn randomly from the box and is returned to the box with another ball of the same colour. The probability that the second ball drawn from the box is blue,is

$U_1, U_2, U_3$ are three urns. $U_1$ contains $5$ red,$3$ white,$2$ black balls; $U_2$ contains $4$ red,$4$ white,$2$ black balls and $U_3$ contains $3$ red,$4$ white,$3$ black balls. If a ball is chosen at random from an urn chosen at random,then the probability of not getting a black ball is

Functions are formed from the set $A = \{a_1, a_2, a_3\}$ to another set $B = \{b_1, b_2, b_3, b_4, b_5\}$. If a function is selected at random, the probability that it is a one-one function is

Box $1$ contains three cards bearing numbers $1, 2, 3$; box $2$ contains five cards bearing numbers $1, 2, 3, 4, 5$; and box $3$ contains seven cards bearing numbers $1, 2, 3, 4, 5, 6, 7$. $A$ card is drawn from each of the boxes. Let $x_i$ be the number on the card drawn from the $i^{\text{th}}$ box,$i = 1, 2, 3$.
$1.$ The probability that $x_1 + x_2 + x_3$ is odd is:
$(A) \frac{29}{105}$ $(B) \frac{53}{105}$ $(C) \frac{57}{105}$ $(D) \frac{1}{2}$
$2.$ The probability that $x_1, x_2, x_3$ are in an arithmetic progression is:
$(A) \frac{9}{105}$ $(B) \frac{10}{105}$ $(C) \frac{11}{105}$ $(D) \frac{7}{105}$
Give the answers for question $1$ and $2$.

Two squares are chosen one by one on a chessboard. The probability that they have a side in common is

In a single throw of three dice,the probability of getting a sum at least $5$ is