In a single throw of two dice,what is the probability of getting a total of $13$?

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

If $A$ and $B$ are two events such that $P(A) = \frac{1}{4}$,$P(B) = \frac{1}{2}$,and $P(A \cap B) = \frac{1}{8}$,find $P(\text{not } A \text{ and not } B)$.

Three identical dice are rolled. The probability that the same number will appear on each of them is:

Two cards are drawn from a pack of $52$ cards. What is the probability that both cards are red or both cards are kings?

$A$ fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. Find the probability that the sum of the numbers that turn up is $12$.