Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is $6$

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 $\leq 5$

Describe the events $A \cap B^{\prime} \cap C^{\prime}$

In a single throw of two dice, the probability of getting more than $7$ is

The chance of throwing a total of $7$ or $12$ with $2$ dice, is

$2$ boys and $2$ girls are in Room $X$, and $1$ boy and $3$ girls in Room $Y$. Specify the sample space for the experiment in which a room is selected and then a person.