Bismuth has a half-life period of $5 \text{ days}$. $A$ sample originally has a mass of $1000 \text{ mg}$. What is the mass of Bismuth remaining after $30 \text{ days}$ (in $.625$)?

In an examination,there are $10$ true-false type questions. Out of $10$,a student can guess the answer of $4$ questions correctly with probability $\frac{3}{4}$ and the remaining $6$ questions correctly with probability $\frac{1}{4}$. If the probability that the student guesses the answers of exactly $8$ questions correctly out of $10$ is $\frac{27 k}{4^{10}}$,then $k$ is equal to

The number of trials conducted in a binomial distribution is $n = 6$. If the difference between the mean and variance of this variate is $\frac{27}{8}$,then the probability of getting at most $2$ successes is:

The probability of a shooter hitting a target is $\frac{3}{4}$. What is the minimum number of times he/she must fire so that the probability of hitting the target at least once is greater than $0.99$?

If the mean and variance of a binomial variable $X$ are $2.4$ and $1.44$ respectively,then the parameters $n$ and $p$ are respectively

$A$ fair coin is tossed a fixed number of times. If the probability of getting $7$ heads is equal to the probability of getting $9$ heads,then the probability of getting $2$ heads is: