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 $10$ ticket.

A bag contains $3$ white and $5$ black balls. If one ball is drawn, then the probability that it is black, is

Two digits are selected randomly from the set $\{1, 2,3, 4, 5, 6, 7, 8\}$ without replacement one by one. The probability that minimum of the two digits is less than $5$ is

Let $S=\{1,2,3,4,5,6\} .$ Then the probability that a randomly chosen onto function $\mathrm{g}$ from $\mathrm{S}$ to $\mathrm{S}$ satisfies $g(3)=2 g(1)$ is :

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$, is

A seven digit number is formed using digits $3 ,3,4,4,4,5,5 .$ The probability, that number so formed is divisible by $2,$ is ..... .