An ellipse is inscribed in a circle and a point within the circle is chosen at random. If the probability that this point lies outside the ellipse is $2/3$,then the eccentricity of the ellipse is:

$A$ bag contains $4$ red and $5$ black balls. Another bag contains $3$ red and $6$ black balls. If one ball is drawn from the first bag and two balls are drawn from the second bag at random,the probability that out of the three balls,two are black and one is red,is

If a year is chosen at random from the years having $53$ Sundays and $53$ Mondays,what is the probability that it is a leap year?

If $A$ and $B$ are two events,then the probability of the event that at most one of $A$ and $B$ occurs is:

If $P(B) = \frac{3}{4}$,$P(A \cap B \cap \bar{C}) = \frac{1}{3}$ and $P(\bar{A} \cap B \cap \bar{C}) = \frac{1}{3}$,then $P(B \cap C)$ 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 $2$.