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

When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is

A bag contains tickets numbered from $1$ to $20$. Two tickets are drawn. The probability that both the numbers are prime, is

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

A bag contains $4$ white, $5$ red and $6$ black balls. If two balls are drawn at random, then the probability that one of them is white is