If $3$ is the variance of a Poisson distribution,then $P(1 < x < 4) = $

The probability of India winning a test match against West Indies is $\frac{1}{2}$. Assuming independence from match to match,the probability that in a $5$ match series India's second win occurs at the third test,is

Three rotten apples are mixed accidentally with seven good apples and four apples are drawn one by one without replacement. Let the random variable $X$ denote the number of rotten apples. If $\mu$ and $\sigma^2$ represent the mean and variance of $X$,respectively,then $10(\mu^2 + \sigma^2)$ is equal to

$A$ fair $n$-faced die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$,then $n=$ (where $n \in N$ ).

Three fair coins with faces numbered $1$ and $0$ are tossed simultaneously. The variance $(X)$ of the probability distribution of random variable $X$,where $X$ is the sum of numbers on the uppermost faces,is

$A$ fair die is tossed twice in succession. If $X$ denotes the number of fours in $2$ tosses,then the probability distribution of $X$ is given by