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

Two digits are selected randomly from the set $\{1, 2,3, 4, 5, 6, 7, 8\}$ without replacement one by one. The probability that minimum of the two digits is less than $5$ is

One of the two events must occur. If the chance of one is $\frac{{2}}{{3}}$ of the other, then odds in favour of the other are

A bag contains $20$ coins. If the probability that bag contains exactly $4$ biased coin is $1/3$ and that of exactly $5$ biased coin is $2/3$,then the probability that all the biased coin are sorted out from the bag in exactly $10$ draws is

Mr. $A$ has six children and atleast one child is a girl, then probability that Mr. $A$ has $3$ boys and $3$ girls, 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 $..........$.