A bag consists of 10 balls each marked with o | vedclass

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

Question

(A) Let $X$ denote the number of balls marked with the digit $0$ among the $4$ balls drawn.Since the balls are drawn with replacement,the trials are B

Vedclass · Accepted Answer

$\left(\frac{9}{10}\right)^{4}$

Vedclass · Answer

(A) Let $X$ denote the number of balls marked with the digit $0$ among the $4$ balls drawn.Since the balls are drawn with replacement,the trials are Bernoulli trials.$X$ follows a binomial distribution with $n=4$ and probability of success $p = \frac{1}{10}$ (drawing a ball marked $0$).The probability of failure is $q = 1 - p = 1 - \frac{1}{10} = \frac{9}{10}$.The probability of $x$ successes is given by $P(X=x) = ^{n}C_{x} \cdot p^{x} \cdot q^{n-x}$.We want the probability that none of the balls is marked with $0$,which is $P(X=0)$.$P(X=0) = ^{4}C_{0} \cdot \left(\frac{1}{10}\right)^{0} \cdot \left(\frac{9}{10}\right)^{4-0}$.$P(X=0) = 1 \cdot 1 \cdot \left(\frac{9}{10}\right)^{4} = \left(\frac{9}{10}\right)^{4}$.

$A$ bag consists of $10$ balls each marked with one of the digits $0$ to $9$. If four balls are drawn successively with replacement from the bag,what is the probability that none is marked with the digit $0$?

Similar Questions

If $X$ has a binomial distribution with parameters $n=6, p$ and $P(X=2)=12, P(X=3)=5$,then $p=$

In a box containing $100$ apples,$10$ are defective. The probability that in a sample of $6$ apples,$3$ are defective is

For a binomial distribution with mean $6$ and variance $2$,the value of $P(X = 8)$ is

If $X \sim B(n, p)$ then $\frac{P(X=k)}{P(X=k-1)}=$

In a box containing $100$ eggs,$10$ eggs are rotten. The probability that out of a sample of $5$ eggs none is rotten if the sampling is with replacement is

Vedclass Test Series

Exam Paper Generator

Online Exam Module