If $8$ coins are tossed simultaneously,then the probability of getting at least $6$ heads is

For a binomial variate $X$ with parameters $n=5$ and $p=\frac{3}{4}$. If $\alpha=\frac{1}{9} P(X \geq 3)$ and $\beta=P(X \leq 2)$,then $256(\beta-\alpha)=$

$A$ and $B$ are playing a chess game with each other. The probability that $A$ wins the game is $0.6$,the probability that he loses is $0.3$,and the probability that it is a draw is $0.1$. If they play three games,what is the probability that $A$ wins at least two games?

On a multiple choice examination with three possible answers for each of the five questions,what is the probability that a candidate would get four or more correct answers just by guessing?

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.

In a Binomial distribution with $n=4$,if $2 P(X=3)=3 P(X=2)$,then the variance is