For the following probability distribution.
| $X$ | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| $P(X)$ | $\frac{1}{10}$ | $\frac{1}{5}$ | $\frac{3}{10}$ | $\frac{2}{5}$ |
$E\left(X^2\right)$ is equal to
Suppose a random variable $X$ follows the Binomial distribution with parameters $n$ and $p$, where $0
In a college, $30 \%$ students fail in Physics, $25 \%$ fail in Mathematics and $10 \%$ fail in both. One student is chosen at random. The probability that she fails in Physics, if she has failed in Mathematics is
$A$ and $B$ are two students. Their chances of solving a problem correctly are $\frac{1}{3}$ and $\frac{1}{4}$, respectively. If the probability of their making a common error is, $\frac{1}{20}$ and they obtain the same answer, then the probability of their answer to be correct is
If a box has 100 pens of which 10 are defective, then what is the probability that out of a sample of 5 pens drawn one by one with replacement atmost one is defective?