An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is

Two different families $A$ and $B$  are blessed with equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket . If the probability that all the tickets go to the children of the family $B$ is $\frac {1}{12}$ , then the number of children in each family is?

If a leap year is selected at random, what is the change that it will contain $53$ Tuesdays ?

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.]

$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

Let $X$ be a set containing $n$ elements. If two subsets $A$ and $B$ of $X$ are picked at random, the probability that $A$ and $B$ have the same number of elements, is