From a class of $12$ girls and $18$ boys, two students are chosen randomly. What is the probability that both of them are girls
$\frac{{22}}{{145}}$
$\frac{{13}}{{15}}$
$\frac{1}{{18}}$
None of these
In a certain lottery $10,000$ tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket.
If $12$ identical balls are to be placed randomly in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is
Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. A fair die is thrown three times. If $r_1, r_2$ and $r_3$ are the numbers obtained on the die, then the probability that $\omega^{I_1}+\omega^{\mathrm{I}_2}+\omega^{\mathrm{I}_3}=0$ is
In a collection of tentickets, there are two winning tickets. From this collection, five tickets are drawn at random Let $p_1$ and $p_2$ be the probabilities of obtaining one and two winning tickets, respectively. Then $p_1+p_2$ lies in the interval
In a lottery, a person choses six different natural numbers at random from $1$ to $20$ , and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [ Hint order of the numbers is not important.]