Bernoulli Trials and Binomial Distribution

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

Let $X$ and $Y$ be two random variables such that $X+Y=100$. If $X$ follows Binomial distribution with parameters $n=100$ and $p=\frac{4}{5}$, what is the variance of $Y$?

The mean and variance of a random variable $X$ having a binomial distribution are $6$ and $3$ respectively. The probability of variable $X$ less than $2$ is

The probability that an event $A$ occurs in a single trial of an experiment is $0.6$. In the first three independent trials of the experiment, the probability that $A$ occurs atleast once is $\dots \dots \dots$

It is possible for a computer to pick up an erroneous signal that does not show up as an error on the screen. The error is called a silent error. A particular terminal is defective and when while using the system "word processor" it introduces a silent paging error with probability $0.1$. The word processor is used $20$ times during a given week.Then the probability that no silent paging errors occus is 

A fair coin is tossed $9$ times. Find the probability that it shows heads exactly $5$ times.

Let $X~B\left(n, p\right), \text{If} n=10, E\left(X\right)=5,$ then find $p$.

A fair coin is tossed $9$ times. The probability that it shows head exactly $5$ times is

A fair coin is tossed $8$ times. Find the probability that it shows heads at least once.

A fair coin is tossed $8$ times. Find the probability that it shows head exactly $5$ times.

If $\mu$ and ${\sigma }^2$ are mean and variance of a random variable $X$ whose $\mathrm{p}.\mathrm{m}.\mathrm{f}.$ is given by $P\left(X=x\right)=\left(\frac{6}{x}\right){\left(\frac{1}{3}\right)}^x{\left(\frac{2}{3}\right)}^{6-x}, x=0, 1, 2, 3\dots \dots 6$, then the value of $2\mu +12{\sigma }^2=$

The probability that bomb will miss the target is $0.2$. Then the probability that out of $10$ bombs dropped exactly $2$ will hit the target is

If $x$ is a binomial variate with mean $6$ and variance $2$, then the value of $P\left(5\le x\le 7\right)$ is

If the mean and variance of a Binomial variable $X$ are $\frac{5}{2}$ and $\frac{5}{4}$ respectively, then $P(X>1)=$

In $3$ trials of a binomial distribution, the probability of $2$ successes is $9$ times the probability of $3$ successes. Then, the probability of success in each trial is

Fifteen coupons are numbered $1,2......15$ 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

A man takes a step forward with probability $0.4$ and backwards with probability $0.6$. The probability that at the end of $11$ steps he is one step away from the starting point is

Probability of $n$ heads in $2n$ tosses of a fair coin is given by