Four fair dice are thrown independently 27 ti | vedclass

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

Question

(A) Let $X$ be the number of dice showing a $3$ or a $5$ in a single throw of $4$ dice. The probability of getting a $3$ or a $5$ on a single die is $

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(A) Let $X$ be the number of dice showing a $3$ or a $5$ in a single throw of $4$ dice. The probability of getting a $3$ or a $5$ on a single die is $p = \frac{2}{6} = \frac{1}{3}$.Thus,the probability of not getting a $3$ or a $5$ is $q = 1 - \frac{1}{3} = \frac{2}{3}$.Since the dice are independent,$X$ follows a binomial distribution $B(n=4, p=1/3)$.The probability that at least two dice show a $3$ or a $5$ is $P(X \geq 2) = 1 - P(X=0) - P(X=1)$.$P(X=0) = { }^4 C_0 (\frac{1}{3})^0 (\frac{2}{3})^4 = 1 	imes 1 	imes \frac{16}{81} = \frac{16}{81}$.$P(X=1) = { }^4 C_1 (\frac{1}{3})^1 (\frac{2}{3})^3 = 4 	imes \frac{1}{3} 	imes \frac{8}{27} = \frac{32}{81}$.$P(X \geq 2) = 1 - (\frac{16}{81} + \frac{32}{81}) = 1 - \frac{48}{81} = \frac{33}{81} = \frac{11}{27}$.The experiment is performed $27$ times. The expected number of times is $E = n 	imes P = 27 	imes \frac{11}{27} = 11$.

Four fair dice are thrown independently $27$ times. Then the expected number of times,at least two dice show up a $3$ or a $5$ is

Similar Questions

Let a random variable $X$ have a Binomial distribution with mean $8$ and variance $4$. If $P(X \leqslant 2) = \frac{k}{2^{16}}$,then $k$ is equal to:

$A$ multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is:

If the standard deviation of the random variable $X$ is $\sqrt{3pq}$ and the mean is $3p$,then $E(X^2) = . . . . . . .$

If $X$ and $Y$ are two independent binomial variates,satisfying $B(10, 1/2)$ and $B(8, 1/2)$ respectively,then the probability $P(X + Y = 2)$ is

If $X \sim B(5, p)$ is a binomial variate such that $P(X=3)=P(X=4)$,then $P(|X-3| < 2)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module