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

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

The probability that a student entering a university will graduate is $0.4$. Find the probability that out of $3$ students of the university all will graduate.

The probability that a student entering a university will graduate is $0.4$. Find the probability that out of $3$ students of the university only one will graduate.

A coin is tossed $999$ times. If $X$ is the number of times heads appeared, then $P(X=r)$ if maximum when $r=$

The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least $0.96$, is

In five throws with a pair of dice, what is the probability of throwing doublets at least thrice?

An unbiased coin is tossed $6$ times. Find, using binomial distribution, the probability of getting at least 5 heads.

Suppose $X$ follows a binomial distribution with parameters $n=6$ and $p$. If $16P(X=4)=P(X=2)$, then $8p$ is equal to

The probability of hitting a target in any shot is $0.2$. If $10$ shots are fired, find the probability that the target will be hit at least twice.

Given that $\mathrm{X}~\mathrm{B}\left(\mathrm{n}=10,\mathrm{p}\right)$. If $\mathrm{E}\left(\mathrm{X}\right)=8$ find the value of $\mathrm{p}$.

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 radar complex consists of eight units that operate independently. The probability that a unit detects an incoming missile is $0.9$.If the probability that an incoming missile will not be detected by any unit is $a^{-8}$, then find $a$.

If $E\left(X\right)=5$ and  $Var\left(X\right)=2.5$, find $n+p$.

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 $p$.

The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least $0.96$, is

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