Bernoulli Trials 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

Five cards are drawn successively, with replacement, from a well-shuffled deck of $52$ cards. The probability that only $3$ cards are spades is

There are $4\%$ defective items in a large bulk of items. What is the probability that a sample of $15$ items will not include more than one defective item?

A bag contains $11$ balls numbered from $1$ to $11$. Suppose an odd number is considered as a 'success'. If two balls are drawn with replacement from the bag. then the probability of getting exactly one success is

A fair $6$-sided die, with $4$ yellow faces and $2$ red faces, is tossed three times and the colour of the top face is noted. Let $Y$ be the number of times the top face is yellow. If $m$ is the mean of $Y,$ and $v$ its variance, then

Consider a random variable $X$ taking values $0, 1, 2, \dots ,n.$ If $k$ is a constant such that $P(X=x)={}^{n}C_x·k$ for $0\le x\le n,$ then $k=$

There are $12$ white and $12$ red balls in a bag. Balls are drawn one by one with replacement from the bag. The probability that $7^{\mathrm{th}}$ drawn ball is $4^{\mathrm{th}}$ white is

One hundred identical coins, each with probability $p$, of showing up a head, are tossed. If $0<p<1$, and if the probability of heads on exactly $50$ coin is equal to that of heads on exactly $51$ coins, then the value of $p$, is

The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students, four are swimmers is

If the mean and variance of a binomial variate $X$ are $2$ and $1$ respectively, then $P\left(X\ge 1\right)$ is

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

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 $\dots \dots \dots$

A man takes a step forward with probability $0.6$ and one step backward with probability $0.4$, then the probability that at the end of eleven steps he is one step away from the starting point is

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