Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. The probability that ${a^2} - {b^2}$ is divisible by $3$ is
$\frac{9}{{87}}$
$\frac{{12}}{{87}}$
$\frac{{15}}{{87}}$
$\frac{{47}}{{87}}$
A box contains $10$ red balls and $15$ green balls. If two balls are drawn in succession then the probability that one is red and other is green, is
A word consists of $11$ letters in which there are $7$ consonants and $4$ vowels. If $2$ letters are chosen at random, then the probability that all of them are consonants, is
Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to through $9$ from both dice will be avoided the prize. If $A$ throws first then the probability that $B$ wins the game is
A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man ?
A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is :