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

$6$ coins are tossed $320$ times. The probability of getting $5$ heads $2$ times 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

$A$ coin is tossed successively three times. The probability of getting exactly one head or $2$ heads is:

If $X \sim B(35, p)$ such that $7 P(X=0)=P(X=1)$,then the value of $\frac{P(X=15)}{P(X=20)}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module