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 drawer contains $5$ brown socks and $4$ blue socks well mixed. A man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match

A cricket team has $15$ members, of whom only $5$ can bowl. If the names of the $15$ members are put into a hat and $11$ drawn at random, then the chance of obtaining an eleven containing at least $3$ bowlers is

There are $n$ letters and $n$ addressed envelops. The probability that each letter takes place in right envelop is

Two integers are selected at random from the set $\{1, 2, …, 11\}.$ Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is

A seven digit number is formed using digits $3 ,3,4,4,4,5,5 .$ The probability, that number so formed is divisible by $2,$ is ..... .