Three unbiased coins are tossed. Then,the probability of getting at most two heads is

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

When two dice are thrown simultaneously,find the probability of the following:
$(1)$ The numbers are the same.
$(2)$ The difference between the numbers is $1$.

When three coins are tossed simultaneously,what is the probability of getting a head on the first,a tail on the second,and a head on the third?

Describe the sample space for the indicated experiment: $A$ coin is tossed and a die is thrown.

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
$A:$ the sum is greater than $8$.
$B:$ $2$ occurs on either die.
$C:$ the sum is at least $7$ and a multiple of $3$.
Which pairs of these events are mutually exclusive?