Embibe Experts Solutions for Exercise 1: SAT 2021

If two dice are thrown together, the probability that the difference of the numbers appearing on them is a prime number

A number is picked up at random from the numbers from $1$ to $1000$. The probability that it is of the form $m^n (\mathrm{where} m>1, n>1)$ is

Consider the collection of points $\left(a,b\right)$ in the coordinate plane such that $a$ and $b$ are integers such that$-5\le a\le 5\text{ and }-5\le b\le 5$. A point is selected at random from the collection. What is the probability that the selected point is at a distance of at most $2$ units from the origin?