Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. Then the probability that $a^2 - b^2$ is divisible by $3$ is (in $/87$)

$2$ boys and $2$ girls are in Room $X$,and $1$ boy and $3$ girls are in Room $Y$. Specify the sample space for the experiment in which a room is selected and then a person.

There are $5$ horses in a race. Mr. $A$ selects $2$ horses at random and bets on them. What is the probability that the winning horse is among the horses selected by Mr. $A$ (in $/5$)?

Let two fair dice $A$ and $B$ be thrown. What is the probability that the number appearing on dice $A$ is greater than the number appearing on dice $B$?

If a leap year is selected at random,what is the chance that it will contain $53$ Tuesdays?

$A$ batch of pencils contains $12$ good,$6$ slightly defective,and $2$ very defective pencils. If a pencil is selected at random,what is the probability that it is a non-defective pencil?