A pair of dice is thrown 4 times. If getting | vedclass

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

Question

(A) The repeated tosses of a pair of dice are Bernoulli trials. Let $X$ denote the number of times of getting doublets in an experiment of throwing tw

Vedclass · Accepted Answer

$\frac{25}{216}$

Vedclass · Answer

(A) The repeated tosses of a pair of dice are Bernoulli trials. Let $X$ denote the number of times of getting doublets in an experiment of throwing two dice simultaneously $4$ times. Probability of getting doublets in a single throw of the pair of dice is $p = \frac{6}{36} = \frac{1}{6}$. Therefore,$q = 1 - p = 1 - \frac{1}{6} = \frac{5}{6}$. Clearly,$X$ has the binomial distribution with $n = 4$,$p = \frac{1}{6}$,and $q = \frac{5}{6}$. The probability of $x$ successes is given by $P(X = x) = ^{n}C_{x} q^{n-x} p^{x}$. For $x = 2$: $P(X = 2) = ^{4}C_{2} \cdot (\frac{5}{6})^{4-2} \cdot (\frac{1}{6})^{2}$ $P(X = 2) = 6 \cdot (\frac{5}{6})^{2} \cdot (\frac{1}{6})^{2}$ $P(X = 2) = 6 \cdot \frac{25}{36} \cdot \frac{1}{36}$ $P(X = 2) = 6 \cdot \frac{25}{1296} = \frac{25}{216}$.

$A$ pair of dice is thrown $4$ times. If getting a doublet is considered a success,find the probability of two successes.

Similar Questions

If the mean and variance of a binomial variable $X$ are $2$ and $1$ respectively, then $P(X \geq 1)$ is equal to

There are $800$ families with four children in each family. Assuming an equal chance for every child to be a boy or a girl,the number of families expected to have children of both sexes is:

$A$ pair of dice is thrown $6$ times. What is the probability of getting a $4$ exactly seven times?

$A$ die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

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