If a random variable X sim Bleft(n=5, p=frac{ | vedclass

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

Question

(B) Given that $X$ follows a binomial distribution $B(n, p)$ with $n=5$ and $p=\frac{1}{3}$.Since $q = 1 - p$,we have $q = 1 - \frac{1}{3} = \frac{2}{

Vedclass · Accepted Answer

$\frac{40}{243}$

Vedclass · Answer

(B) Given that $X$ follows a binomial distribution $B(n, p)$ with $n=5$ and $p=\frac{1}{3}$.Since $q = 1 - p$,we have $q = 1 - \frac{1}{3} = \frac{2}{3}$.The probability mass function is given by $P(X=k) = { }^n C_k p^k q^{n-k}$.We need to find $P(2 Substituting the values into the formula:$P(X=3) = { }^5 C_3 \left(\frac{1}{3}ight)^3 \left(\frac{2}{3}ight)^{5-3}$$P(X=3) = \frac{5 	imes 4}{2 	imes 1} 	imes \left(\frac{1}{27}ight) 	imes \left(\frac{2}{3}ight)^2$$P(X=3) = 10 	imes \frac{1}{27} 	imes \frac{4}{9}$$P(X=3) = \frac{40}{243}$

If a random variable $X \sim B\left(n=5, p=\frac{1}{3}\right)$,then $P(2 < X < 4) = $

Similar Questions

If there are $n$ independent trials,$p$ and $q$ are the probability of success and failure respectively,then what is the probability of exactly $r$ successes?

The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least $0.96$ is:

If $X$ has a binomial distribution with mean $np$ and variance $npq$,then $\frac{P(X = k)}{P(X = k - 1)}$ is

If $X$ has a binomial distribution with parameters $n=6, p$ and $P(X=2)=12, P(X=3)=5$,then $p=$

Ten eggs are drawn successively with replacement from a lot containing $10 \%$ defective eggs. Find the probability that there is at least one defective egg.

Vedclass Test Series

Exam Paper Generator

Online Exam Module