Two dice are thrown three times. What is the probability that the first throw shows $10$,the second throw shows $11$,and the third throw shows $12$?

In a non-leap year, the probability of getting $53$ Sundays or $53$ Tuesdays or $53$ Thursdays is:

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment:
$A:$ the sum is even.
$B:$ the sum is a multiple of $3$.
$C:$ the sum is less than $4$.
$D:$ the sum is greater than $11$.
Which pairs of these events are mutually exclusive?

$A$ family with three children is chosen at random. The probability that the oldest and youngest children are of the same gender is

$A$ man and his wife appear in an interview for two vacancies. The probability of the husband's selection is $1/7$ and the probability of the wife's selection is $1/5$. What is the probability that only one of them is selected?

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A$ and $B$ are mutually exclusive and exhaustive.