The probability that a non-leap year selected at random will contain $52$ Saturdays or $53$ Sundays is

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 $1$.

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

Three coins are tossed once. Let $A$ denote the event 'three heads show',$B$ denote the event 'two heads and one tail show',$C$ denote the event 'three tails show',and $D$ denote the event 'a head shows on the first coin'. Which events are mutually exclusive?

If two subsets $A$ and $B$ are selected at random from a set $S$ containing $n$ elements,then the probability that $A \cap B = \phi$ and $A \cup B = S$ is

Two numbers $x$ and $y$ are chosen at random from the set of integers $\{1, 2, 3, 4, \dots, 15\}$. The probability that the point $(x, y)$ lies on a line passing through $(0, 0)$ with a slope of $\frac{2}{3}$ is: