The records of a hospital show that $10\%$ of the cases of a certain disease are fatal. If $6$ patients are suffering from the disease,then the probability that only three will die is

An urn contains $25$ balls,of which $10$ balls bear a mark $'X'$ and the remaining $15$ bear a mark $'Y'$. $A$ ball is drawn at random from the urn,its mark is noted down,and it is replaced. If $6$ balls are drawn in this way,find the probability that at least one ball will bear the $'Y'$ mark.

If a random variable $X$ follows the Binomial distribution $B(10, p)$ such that $5 P(X=0) = P(X=1)$,then the value of $\frac{P(X=5)}{P(X=6)}$ is equal to

Consider $5$ independent Bernoulli trials,each with a probability of success $p$. If the probability of at least one failure is greater than or equal to $31/32$,then in which interval does $p$ lie?

$A$ person fails $4$ times in a game when he plays $9$ times. If he plays $15$ times, the probability of having success at most one is

An urn contains $25$ balls of which $10$ balls bear a mark $'X'$ and the remaining $15$ bear a mark $'Y'$. $A$ ball is drawn at random from the urn,its mark is noted down and it is replaced. If $6$ balls are drawn in this way,find the probability that all will bear $'X'$ mark.