Two dice are thrown simultaneously. If $X$ denotes the number of sixes,then the expectation of $X$ is

In a tournament,a team plays $10$ matches with probabilities of winning and losing each match as $\frac{1}{3}$ and $\frac{2}{3}$ respectively. Let $x$ be the number of matches that the team wins,and $y$ be the number of matches that the team loses. If the probability $P(|x-y| \leq 2)$ is $p$,then $3^9 p$ equals....................

Ten eggs are drawn successively with replacement from a lot containing $10 \%$ defective eggs. Find the probability that there is at least one defective egg.

Two cards are drawn at random one after the other with replacement from a pack of playing cards. If $X$ is the random variable denoting the number of ace cards drawn, then the mean of the probability distribution of $X$ is

If the probability that a student selected at random from a particular college is good at mathematics is $0.6$, then the probability of having exactly two students who are good at mathematics in a group of $8$ students of that college is:

The mean and variance of a binomial variable $X$ are $2$ and $1$ respectively. The probability that $X$ takes values greater than $1$ is: