If X follows a binomial distribution with par | vedclass

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

Question

(C) The probability mass function of a binomial distribution is given by $P(X = k) = {}^nC_k p^k q^{n-k}$,where $q = 1 - p$.Given $n = 6$,we have $P(X

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(C) The probability mass function of a binomial distribution is given by $P(X = k) = {}^nC_k p^k q^{n-k}$,where $q = 1 - p$.Given $n = 6$,we have $P(X = 4) = {}^6C_4 p^4 q^2$ and $P(X = 2) = {}^6C_2 p^2 q^4$.According to the given condition,$9P(X = 4) = P(X = 2)$.Substituting the values,we get $9 	imes {}^6C_4 p^4 q^2 = {}^6C_2 p^2 q^4$.Since ${}^6C_4 = \frac{6 	imes 5}{2 	imes 1} = 15$ and ${}^6C_2 = \frac{6 	imes 5}{2 	imes 1} = 15$,the equation becomes $9 	imes 15 p^4 q^2 = 15 p^2 q^4$.Dividing both sides by $15 p^2 q^2$ (assuming $p, q 
eq 0$),we get $9p^2 = q^2$.Taking the square root of both sides,$3p = q$.Since $q = 1 - p$,we have $3p = 1 - p$,which implies $4p = 1$.Therefore,$p = \frac{1}{4}$.

If $X$ follows a binomial distribution with parameters $n = 6$ and $p$. If $9P(X = 4) = P(X = 2)$,then $p = $

Similar Questions

$A$ fair coin is tossed $15$ times. The probability that the tail will appear at least thrice is

One hundred identical coins,each with probability $p$ of showing up heads,are tossed once. If $0 < p < 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins,then the value of $p$ is

$A$ die is thrown $10$ times. The probability that an odd number will come up at least once is

An irregular six-faced die is thrown. The probability that in $5$ throws it will give $3$ even numbers is twice the probability that it will give $2$ even numbers. The number of times,in $6804$ sets of $5$ throws,you expect to get no even number is:

The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. Find the probability that out of $5$ such bulbs,at least one will fuse after $150$ days.

Vedclass Test Series

Exam Paper Generator

Online Exam Module