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

For Binomial distribution $B \left(10, \frac{1}{2} \right)$,if $P(X \leq 2) = m \left( \frac{1}{2} \right)^{10}$,then $m =$ . . . . . . .

$A$ die is tossed twice. Getting a number greater than $4$ is considered a success. Then the variance of the probability distribution of the number of successes is

From a lot of $30$ bulbs which include $6$ defectives,a sample of $4$ bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

Among every $8$ units of a product, one is likely to be defective. If a consumer has ordered $5$ units of that product, then the probability that at most one unit is defective among them is

An unbiased coin is tossed to get $2$ points for turning up a head and $1$ point for the tail. If three unbiased coins are tossed simultaneously, then the probability of getting a total of an odd number of points 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?