The probability of a sure event is

When two dice are thrown simultaneously,what is the probability that at least one of the dice shows a number greater than $3$?

Mr. $A$ has $6$ children and at least one child is a girl. What is the probability that Mr. $A$ has $3$ boys and $3$ girls?

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

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.

Two integers $x$ and $y$ are chosen with replacement from the set $\{0, 1, 2, 3, \ldots, 10\}$. Then the probability that $|x-y| > 5$ is: