The probability of getting $4$ heads in $8$ throws of a coin, 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

Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$, respectively. Suppose $\alpha$ is the number of heads that appear when $C _1$ is tossed twice, independently, and suppose $\beta$ is the number of heads that appear when $C _2$ is tossed twice, independently, Then probability that the roots of the quadratic polynomial $x^2-\alpha x+\beta$ are real and equal, is

If $4 \,-$ digit numbers greater than $5,000$ are randomly formed from the digits $0,\,1,\,3,\,5,$ and $7,$ what is the probability of forming a number divisible by $5$ when, the digits are repeated ?

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.

Four distinct numbers are randomly selected out of the set of first $20$ natural numbers. Probability that no two of them are consecutive is -