Vinod Singh and Shweta Pawar Solutions for Chapter: Binomial Distribution, Exercise 4: Evaluation Test

A die is thrown $100$ times. If getting an odd number is considered a success, the variance of the number of successes is

In eight throws of a die $1$ or $3$ is considered a success. Then the standard deviation of the success is

Consider $5$ independent Bernoulli's trials each with probability of success $p.$ If the probability of at least one failure is greater than or equal to $\frac{31}{32},$ then $p$ lies in the interval

A coin is tossed $3$ times by $2$ persons. The probability that both get the equal number of heads is

In a binomial distribution $B\left(n, p=\frac{1}{4}\right).$ If the probability of at least one success is greater than or equal to $\frac{9}{10},$ then $n$ is greater than

The sum of the mean and variance of a binomial distribution is $15$ and the sum of their squares is $117.$ The mean of the distribution is 

In a trial, the probability of success is twice the probability of failure. In six trials the probability of at least four successes will be

The mean and variance of a binomial distribution $(p+q{)}^n$ are $20$ and $16$, respectively. Then, the pair $(n,p)$ is