For a binomial distribution with mean 6 and v | vedclass

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

Question

(C) Given mean $= np = 6$ ...$(i)$ Variance $= npq = 2$ ...(ii) Dividing (ii) by $(i)$,we get $q = \frac{2}{6} = \frac{1}{3}$. Since $p + q = 1$,we ha

Vedclass · Accepted Answer

$1-\frac{19}{3^9}$

Vedclass · Answer

(C) Given mean $= np = 6$ ...$(i)$ Variance $= npq = 2$ ...(ii) Dividing (ii) by $(i)$,we get $q = \frac{2}{6} = \frac{1}{3}$. Since $p + q = 1$,we have $p = 1 - \frac{1}{3} = \frac{2}{3}$. Substituting $p$ in $(i)$,$n 	imes \frac{2}{3} = 6 \Rightarrow n = 9$. We need to find $P(X \geq 2) = 1 - [P(X=0) + P(X=1)]$. $P(X=0) = {}^9C_0 	imes (\frac{2}{3})^0 	imes (\frac{1}{3})^9 = \frac{1}{3^9}$. $P(X=1) = {}^9C_1 	imes (\frac{2}{3})^1 	imes (\frac{1}{3})^8 = 9 	imes \frac{2}{3} 	imes \frac{1}{3^8} = \frac{18}{3^9}$. $P(X \geq 2) = 1 - [\frac{1}{3^9} + \frac{18}{3^9}] = 1 - \frac{19}{3^9}$.

For a binomial distribution with mean $6$ and variance $2$,find $P(X \geq 2)$.

Similar Questions

$A$ 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 urn contains $25$ balls of which $10$ balls bear a mark $'X'$ and the remaining $15$ bear a mark $'Y'$. $A$ ball is drawn at random from the urn,its mark is noted down and it is replaced. If $6$ balls are drawn in this way,find the probability that not more than $2$ will bear $'Y'$ mark.

$A$ bag contains books numbered $1$ to $20$. Three books are drawn from the bag with replacement. The probability that the largest number on the books is $7$ 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

If the mean and variance of a binomial distribution are $4$ and $2$ respectively,then the probability of getting $2$ successes is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module