$A$ fair coin is tossed $K$ times such that the probability of getting $4$ heads is equal to that of getting $6$ heads. If the probability is maximum for getting $r$ heads, then $r=$

$A$ coin is tossed $3$ times by $2$ persons. What is the probability that both get an equal number of heads?

$A$ shooter can hit a given target with probability $\frac{1}{4}$. She keeps firing a bullet at the target until she hits it successfully three times and then she stops firing. The probability that she fires exactly six bullets lies in the interval

For a binomial variate $X$, if $n=4$ and $P(X=4)=6 P(X=2)$, then the value of $p$ 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 colour is $q$. If $p : q = m : n$,where $m$ and $n$ are coprime,then $m + n$ is equal to $..........$.

$A$ rifle man is firing at a distant target and has only $10\%$ chance of hitting it. The minimum number of rounds he must fire in order to have $50\%$ chance of hitting it at least once is