When three identical dice are thrown,what is the probability of getting the same number on each of them?

Describe the sample space for the indicated experiment: $A$ coin is tossed three times.

Two dice are thrown simultaneously. The probability of getting the sum $2$,$8$,or $12$ is

$A, B$ and $C$ are mutually exclusive events. If $P(A) = \frac{3x + 1}{3}$,$P(B) = \frac{1 - x}{4}$,and $P(C) = \frac{1 - 2x}{2}$,then the possible values of $x$ lie in the interval ...

If $A$ and $B$ are events such that $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(\overline{A}) = \frac{2}{3}$,then what is the value of $P(\overline{A} \cap B)$?

$A, B, C$ are any three events. If $P(S)$ denotes the probability of $S$ happening,then $P(A \cap (B \cup C)) = $