The probability of success p for the Binomial | vedclass

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

Question

(D) For a Binomial distribution,$P(X=k) = {}^nC_k p^k q^{n-k}$,where $q = 1-p$.Given $n=6$,the relation is $4 P(X=4) = P(X=2)$.Substituting the formul

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(D) For a Binomial distribution,$P(X=k) = {}^nC_k p^k q^{n-k}$,where $q = 1-p$.Given $n=6$,the relation is $4 P(X=4) = P(X=2)$.Substituting the formula: $4 \cdot {}^6C_4 p^4 q^{6-4} = {}^6C_2 p^2 q^{6-2}$.$4 \cdot {}^6C_4 p^4 q^2 = {}^6C_2 p^2 q^4$.Since ${}^6C_4 = {}^6C_2 = 15$,we have:$4 \cdot 15 \cdot p^4 q^2 = 15 \cdot p^2 q^4$.Dividing both sides by $15 p^2 q^2$ (assuming $p, q 
eq 0$):$4 p^2 = q^2$.Taking the square root on both sides: $2p = q$.Since $p + q = 1$,we substitute $q = 2p$:$p + 2p = 1 \Rightarrow 3p = 1 \Rightarrow p = \frac{1}{3}$.

The probability of success $p$ for the Binomial distribution satisfying the relation $4 P(X=4) = P(X=2)$ with parameter $n=6$ is

Similar Questions

The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. What is the probability that out of $5$ such bulbs,not more than one will fuse?

$A$ die is thrown $100$ times. The standard deviation of getting an even number is:

For which binomial distribution are the mean $= 6$ and variance $= 2$?

For a binomial variate $X$ with $n=6$,if $P(X=2)=9 P(X=4)$,then its variance is

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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module