A fair coin is tossed $100$ times. The probability of getting tails an odd number of times is

$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and one spade?

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

Find the probability that when a hand of $7$ cards is drawn from a well shuffled deck of $52$ cards, it contains atleast $3$ Kings.

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is $q$. If $p : q = m$ $: n$, where $m$ and $n$ are coprime, then $m + n$ is equal to $..........$.

A fair dice is thrown up to $20$ times. The probability that on the $10^{th}$ throw, the fourth six apears is :-