Consider the following events:E_1: Six fair d | vedclass

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

Question

(A) For event $E_1$,six fair dice are rolled. The probability that no die shows a six is $(\frac{5}{6})^6$. Thus,$p_1 = 1 - (\frac{5}{6})^6 = 1 - 0.33

Vedclass · Accepted Answer

$p_1 > p_2$

Vedclass · Answer

(A) For event $E_1$,six fair dice are rolled. The probability that no die shows a six is $(\frac{5}{6})^6$. Thus,$p_1 = 1 - (\frac{5}{6})^6 = 1 - 0.3349 = 0.6651$.For event $E_2$,twelve fair dice are rolled. Let $X$ be the number of dice showing a six. $X$ follows a binomial distribution $B(n=12, p=\frac{1}{6})$.$p_2 = P(X \geq 2) = 1 - [P(X=0) + P(X=1)]$.$P(X=0) = (\frac{5}{6})^{12} \approx 0.1122$.$P(X=1) = \binom{12}{1} (\frac{1}{6})^1 (\frac{5}{6})^{11} = 12 	imes \frac{1}{6} 	imes 0.1346 \approx 0.2692$.$p_2 = 1 - (0.1122 + 0.2692) = 1 - 0.3814 = 0.6186$.Since $0.6651 > 0.6186$,we have $p_1 > p_2$.

Consider the following events:
$E_1$: Six fair dice are rolled and at least one die shows six.
$E_2$: Twelve fair dice are rolled and at least two dice show six.
Let $p_1$ be the probability of $E_1$ and $p_2$ be the probability of $E_2$. Which of the following is true?

Similar Questions

An experiment succeeds twice as often as it fails. Then the probability,that in the next $6$ trials there will be at least $4$ successes,is

If $X \sim B(4, p)$ and $P(X=0)=\frac{16}{81}$,then $P(X=4)=$

For $X \sim B(n, p)$,if $p=0.6$ and $E(X)=6$,then $\operatorname{Var}(X)=$

If the difference between the mean and variance of a binomial variate is $\frac{5}{9}$,then the probability of getting $2$ successes for an event when the experiment is conducted $5$ times,is

If $P$ and $Q$ each toss three coins,the probability that both get the same number of heads is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Consider the following events:$E_1$: Six fair dice are rolled and at least one die shows six.$E_2$: Twelve fair dice are rolled and at least two dice show six.Let $p_1$ be the probability of $E_1$ and $p_2$ be the probability of $E_2$. Which of the following is true?