Binomial and Poisson Distributions

Fifteen coupons are numbered $1, 2, 3,..., 15,$ respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is $9,$ is:

The probability that an event $A$ happens in one trial of an experiment is $0.4$ . Three independent trials of the experiment are performed. The probability that the event $A$ happens at least once is

If $6$ is the mean of a Poisson distribution, then $P\left(X\ge 3\right)=$

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X~B\left(16,0.25\right)$ and $Y~P\left(2\right)$. Then the sum of the variances of $X$ and $Y$ is

Which of the following is not a property of a Binomial distribution?

Find the expectation of number of heads in $30$ tosses of a fair coin.

For a binomial distribution with mean $6$ and variance $2.$ Then the value of $P(X=8$$)$ is

The probability of a man hitting a target is $\frac{2}{3}$. the minimum number of times he must fire so that the probability of hitting the target at least once is more then $90\%$

For a binomial distribution $B\left(n,p\right)$,mean$=200$, standard deviation$=10$, then $n^2+\frac{1}{p^2}+\frac{1}{q^2}=?$

If the mean of a Poisson distribution is $\frac{1}{3},$ then the ratio $P(X=1): P(X=2)$ is

If $X$ is a poisson variate such that $P(X=2)=P(X=3),$ then $e^3·P(X=4)$ is

When employees with smart phones are randomly selected, $50\%$ use them for office purpose. The probability that out of $10$ users exactly $2$ of them use for office purpose is

If $X$ is a poisson variable such that $3P(X=4)=\frac{1}{2}P(X=2)+P(X=0)$ then the mean of $X$ is ________

The mean and variance of a binomial distribution are $5$ and $4$ respectively. Then what is $P(X=1)?$

If the sum of mean and variance of a binomial distribution is $15$ and the sum of their squares is $117$, then the number of independent trials is equal to

The mean and variance of a binomial distribution are $4$ and $3$respectively, then the probability of getting exactly six successes in this distribution is

The mean and variance of a binomial distribution are $4$ and $3$respectively, then the probability of getting exactly six successes in this distribution is

A boy is throwing stones at a target. The probability of hitting the target at any trial is  $\frac{1}{2}$. The probability of hitting the target for the  $5^{\mathrm{th}}$ time at the ${10}^{\mathrm{th}}$ throw, is