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 $..........$.

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 two ticket.

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

The probability of hitting a target by three marks men is $\frac{1}{2} , \frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability that exactly two of them will hit the target is $\lambda$ and that at least two of them hit the target is $\mu$ then $\lambda + \mu$ is equal to :-

Three randomly chosen nonnegative integers $x, y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even, is

If $7$ dice are thrown simultaneously, then probability that all six digit appears on the upper face is equal to -