$A$ box contains $15$ green and $10$ yellow balls. If $10$ balls are randomly drawn,one by one,with replacement,then the variance of the number of green balls drawn is

Let a random variable $X$ have a Binomial distribution with mean $8$ and variance $4$. If $P(X \leqslant 2) = \frac{k}{2^{16}}$,then $k$ is equal to:

$A$ student writes an examination which contains $8$ true or false questions. If he answers $6$ or more questions correctly,he passes the examination. If the student answers all the questions,then the probability that he fails in the examination is

In a multiple-choice examination, there are $10$ questions with one correct option out of $4$ options for each question. $A$ student gets $4$ marks for each correct answer and $1$ mark is deducted for each incorrect answer. The probability that a student, guessing randomly on every question, scores $30$ marks in this exam is... (in $/4^{10}$)

If $A$ and $B$ simultaneously toss one coin each,$50$ times,then the probability of not getting a tail on both the coins in any single toss 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 the number of balls with $'X'$ mark and $'Y'$ mark will be equal.