Bernoulli Trial and Binomial Distribution

Probability distribution is classified as normal if expected return lies between

Range of probability distribution with 95.46% lies within

A marksman hits $75\%$ of all his targets. What is the probability that he will hit exactly four of his next ten shots?

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 $Y$?

Let the probability of getting head for a biased coin be $\frac{1}{4}$. It is tossed repeatedly until a head appears. Let  $N$ be the number of tosses required. If the probability that the equation $64x^2+5Nx+1=0$ has no real root is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q-p$ is equal to..........

The random variable $X$ follows binomial distribution $B(n, p)$, for which the difference of the mean and the variance is $1$.

If $2 P(X=2)=3 P(X=1)$, then $n^{2}P(X>1)$ is equal to

Let a die be rolled $\mathrm{n}$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{k}{2^{15}}$, then $k$ is equal to

A pair of dice is thrown $5$ times. For each throw, a total of $5$ is considered a success. If the probability of at least $4$ successes is $\frac{k}{3^{11}}$, then $k$ is equal to

In a binomial distribution, $B\left(n,p\right)$, the sum and product of the mean and variance are $5$ and $6$ respectively, then find $6\left(n+p-q\right)$ is equal to

For a biased coin, the probability of getting head is $\frac{1}{4}$. It is tossed $n$ times, till we get head. Given a quadratic equation $64x^2+2nx+1=0$. If probability that the quadratic equation has no real roots is $\frac{P}{Q}$ (where, $P$ and $Q$ are co-prime), then the value of $Q-P$ is ________ 

The incidence of suffering from a disease among workers in an industry has a chance of $33\frac{1}{3}\%$. What is the probability that $3$ out of $6$ workers suffering from a disease? 

The probability of an event that Haresh hits the target is $\frac{1}{4}$. He hits targets $25$ times, then its variance is 

In a recreational event at a school, there were $8$ students, $6$ parents, and $4$ teachers. To play a game, two members were selected randomly one after the other. Find the probability distribution of the number of students. Show your steps.

A pair of dice is thrown independently three times. The probability of getting a score of $10$ exactly twice is:

A player $A$ plays a game against a machine. Ay each round he deposits $100 \mathrm{Rs}.$ in the machine and flips a coin. If a coins shows head, $A$ get $100 \mathrm{Rs}.$ increment and if a coins shows tail, then $A$ gets $100 \mathrm{Rs}.$ decrement. Let $A$ start with $1000 \mathrm{Rs}.$, then the probability that he is left with no money by the ${14}^{\mathrm{th}}$ round.

A person takes a step forward with probability $p$ and takes a step backward with probability $q$, where $p+q=1$. The probability that after $\left(2n+1\right)$ steps the person is only one step away from his initial position, is equal to 

A random variable $X$ is binomially distributed with parameter $n=25$ and $p=0.2$. The sknewness of the variable $X$ is