If Mohan has $3$ tickets of a lottery containing $3$ prizes and $9$ blanks,then his chance of winning at least one prize is

Consider the set of all $7$-digit numbers formed by the digits $0, 1, 2, 3, 4, 5, 6$,each chosen exactly once. If a number is randomly drawn from this set,the probability that it is divisible by $4$ is

From $80$ cards numbered $1$ to $80$,two cards are selected randomly. The probability that both the cards have numbers divisible by $4$ is given by

$\omega$ is a complex cube root of unity. When an unbiased die is thrown $3$ times,if $\beta_1, \beta_2, \beta_3$ are the numbers appeared on the die,then the probability that $\beta_1, \beta_2$ and $\beta_3$ satisfy $\omega^{\beta_1}+\omega^{\beta_2}=-\omega^{\beta_3}$ is

If $4$ letters are selected at random from the letters of the word $PROBABILITY$,then the probability of getting a combination of letters in which at least one letter is repeated is

Two numbers $x$ and $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, \dots, 1000\}$. The probability that $|x^4 - y^4|$ is divisible by $5$ is -