If a die is thrown 7 times,what is the probab | vedclass

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

Question

(D) This is a binomial distribution problem where $n = 7$ (number of trials),$k = 4$ (number of successes),$p = \frac{1}{6}$ (probability of getting a

Vedclass · Accepted Answer

$^7{C_4}{\left( {\frac{1}{6}} \right)^4}{\left( {\frac{5}{6}} \right)^3}$

Vedclass · Answer

(D) This is a binomial distribution problem where $n = 7$ (number of trials),$k = 4$ (number of successes),$p = \frac{1}{6}$ (probability of getting a $5$ in a single throw),and $q = 1 - p = \frac{5}{6}$ (probability of not getting a $5$).Using the binomial probability formula $P(X = k) = ^n{C_k} \cdot p^k \cdot q^{n-k}$:$P(X = 4) = ^7{C_4} \cdot \left( \frac{1}{6} \right)^4 \cdot \left( \frac{5}{6} \right)^{7-4}$$P(X = 4) = ^7{C_4} \cdot \left( \frac{1}{6} \right)^4 \cdot \left( \frac{5}{6} \right)^3$Thus,the correct option is $D$.

If a die is thrown $7$ times,what is the probability of getting exactly $5$ four times?

Similar Questions

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(n_1, 0.5)$ and $Y \sim B(n_2, 0.4)$. If the variance of both $X$ and $Y$ is $6$,then $\sqrt{n_1+n_2}=$

If the mean and variance of a binomial distribution are $4$ and $\frac{4}{3}$ respectively, then $P(X=2)=$

Find the probability of throwing at most $2$ sixes in $6$ throws of a single die.

The probability of a bomb hitting a bridge is $\frac{1}{2}$ and two direct hits are needed to destroy it. The least number of bombs required so that the probability of the bridge being destroyed is greater than $0.9$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module