An experiment succeeds twice as often as it f | vedclass

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

Question

(D) Let $p(F) = q$ and $p(S) = p$. Given $p = 2q$. Since $p + q = 1$,we have $2q + q = 1$,which gives $3q = 1$,so $q = \frac{1}{3}$ and $p = \frac{2}{

Vedclass · Accepted Answer

$\frac{256}{729}$

Vedclass · Answer

(D) Let $p(F) = q$ and $p(S) = p$. Given $p = 2q$. Since $p + q = 1$,we have $2q + q = 1$,which gives $3q = 1$,so $q = \frac{1}{3}$ and $p = \frac{2}{3}$. This is a binomial distribution with $n = 6$,$p = \frac{2}{3}$,and $q = \frac{1}{3}$. The probability of at least $5$ successes is $P(X \geq 5) = P(X = 5) + P(X = 6)$. Using the formula $P(X = k) = {^nC_k} p^k q^{n-k}$: $P(X = 5) = {^6C_5} \left(\frac{2}{3}ight)^5 \left(\frac{1}{3}ight)^1 = 6 	imes \frac{32}{243} 	imes \frac{1}{3} = \frac{192}{729}$. $P(X = 6) = {^6C_6} \left(\frac{2}{3}ight)^6 \left(\frac{1}{3}ight)^0 = 1 	imes \frac{64}{729} 	imes 1 = \frac{64}{729}$. Therefore,$P(X \geq 5) = \frac{192}{729} + \frac{64}{729} = \frac{256}{729}$.

An experiment succeeds twice as often as it fails. The probability of at least $5$ successes in the $6$ trials of this experiment is

Similar Questions

In a Binomial distribution,if $n$ is the number of trials and the mean and variance are $4$ and $3$ respectively,then $2^{32} P\left(X=\frac{n}{2}\right)=$

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:

Let $X$ be a binomial variate with parameters $n=6$ and $p$. If $4 P(X=4)=P(X=2)$, then $p$ equals

In a game,a pair of dice is rolled $24$ times. If a person wins the game by not getting $6$ on both the dice in any one of the $24$ rolls,then the probability that a person wins the game is

In order to get a head at least once with probability $\geq 0.9$, the minimum number of times an unbiased coin needs to be tossed is

Vedclass Test Series

Exam Paper Generator

Online Exam Module