In a certain lottery $10,000$ tickets are sold and $10$ equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket?

Three students $X, Y$ and $Z$ appear for an examination. The probability of $X$ passing the examination is $\frac{1}{5}$,the probability of $Y$ passing the examination is $\frac{1}{4}$ and the probability of $Z$ failing the examination is $\frac{2}{3}$. The probability that at least two of them pass the exam is

The probability of getting a number greater than $2$ in throwing a die is

The chance of getting a doublet with $2$ dice is

If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$, $P(\bar{A} \cup \bar{B}) = \frac{7}{10}$, and $P(B) = \frac{2}{5}$, then $P(A)$ equals

$A$ problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4}$ respectively. The probability that the problem is solved, if both of them try independently, is