A bag contains 30 white balls and 10 red ball | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The total number of balls is $30 + 10 = 40$. The probability of drawing a white ball is $p = \frac{30}{40} = \frac{3}{4}$. The probability of draw

Vedclass · Accepted Answer

$4\sqrt{3}$

Vedclass · Answer

(B) The total number of balls is $30 + 10 = 40$. The probability of drawing a white ball is $p = \frac{30}{40} = \frac{3}{4}$. The probability of drawing a red ball is $q = 1 - p = \frac{1}{4}$. The number of trials is $n = 16$. Since the balls are drawn with replacement,$X$ follows a binomial distribution $B(n, p)$. The mean of $X$ is $E(X) = np = 16 	imes \frac{3}{4} = 12$. The standard deviation of $X$ is $\sigma = \sqrt{npq} = \sqrt{16 	imes \frac{3}{4} 	imes \frac{1}{4}} = \sqrt{3}$. Therefore,the ratio is $\frac{	ext{mean}}{	ext{standard deviation}} = \frac{12}{\sqrt{3}} = \frac{12\sqrt{3}}{3} = 4\sqrt{3}$.

$A$ bag contains $30$ white balls and $10$ red balls. $16$ balls are drawn one by one randomly from the bag with replacement. If $X$ is the number of white balls drawn,then $\left( \frac{\text{mean of } X}{\text{standard deviation of } X} \right)$ is equal to

Similar Questions

In a binomial distribution,the probability of success is $\frac{1}{4}$ and the standard deviation is $3$. Then,its mean is

$A$ dice is thrown two times. If getting an odd number is considered a success,then the probability of two successes is

In a Binomial distribution consisting of $5$ independent trials,probabilities of exactly $1$ and $2$ successes are $0.4096$ and $0.2048$ respectively,then the probability of getting exactly $4$ successes is

Let $X$ be a binomially distributed random variable with mean $4$ and variance $\frac{4}{3}$. Then $54 P(X \leq 2)$ is equal to.

The probability that a person wins a prize on a lottery ticket is $\frac{1}{4}$. If he purchases $5$ lottery tickets at random,then the probability that he wins at least one prize is

Vedclass Test Series

Exam Paper Generator

Online Exam Module