The probability that a person is not a sports | vedclass

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Question

(B) Let $p$ be the probability that a person is a sportsperson and $q$ be the probability that a person is not a sportsperson. Given $q = \frac{1}{6}$

Vedclass · Accepted Answer

$6 	imes \left(\frac{5}{6}ight)^5 	imes \frac{1}{6}$

Vedclass · Answer

(B) Let $p$ be the probability that a person is a sportsperson and $q$ be the probability that a person is not a sportsperson. Given $q = \frac{1}{6}$,so $p = 1 - q = 1 - \frac{1}{6} = \frac{5}{6}$. We have $n = 6$ members in the family. We want to find the probability that $x = 5$ members are sportspersons. Using the Binomial distribution formula $P(X = x) = ^nC_x 	imes p^x 	imes q^{n-x}$: $P(X = 5) = ^6C_5 	imes \left(\frac{5}{6}ight)^5 	imes \left(\frac{1}{6}ight)^{6-5}$ $P(X = 5) = 6 	imes \left(\frac{5}{6}ight)^5 	imes \frac{1}{6}$ Thus,the probability is $6 	imes \left(\frac{5}{6}ight)^5 	imes \frac{1}{6}$.

The probability that a person is not a sportsperson is $\frac{1}{6}$. Then the probability that out of the $6$ members of the family,$5$ are sportspersons is

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