If $3$ numbers are chosen from the first $15$ natural numbers,what is the probability that the numbers are in arithmetic progression?

Let $m, n$ be two distinct integers chosen randomly from the set $\{0, 1, 2, \ldots, 99\}$. Then,the probability that $4^m + 4^n + 3$ is divisible by $5$ lies in the interval

In a shoe rack,there are $4$ pairs of shoes. If $4$ shoes are drawn one after the other at random without replacement,what is the probability of getting at least one correct pair of shoes among the four shoes drawn?

Two points are randomly chosen on the circumference of a circle of radius $r$. The probability that the distance between the two points is at least $r$ is equal to

$A$ bag contains $3$ white and $6$ red balls. Four balls are drawn at a time randomly. The probability of getting at least $2$ red balls is:

In a box,there are $2$ red,$3$ black,and $4$ white balls. If $3$ balls are drawn together,what is the probability that they are of the same color?