The probability that a student is a singer is | vedclass

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Question

(B) This is a binomial distribution problem where $n = 5$ and $p = \frac{1}{5}$.The probability of success (student is a singer) is $p = \frac{1}{5}$.

Vedclass · Accepted Answer

$4\left(\frac{1}{5}\right)^4$

Vedclass · Answer

(B) This is a binomial distribution problem where $n = 5$ and $p = \frac{1}{5}$.The probability of success (student is a singer) is $p = \frac{1}{5}$.The probability of failure (student is not a singer) is $q = 1 - p = 1 - \frac{1}{5} = \frac{4}{5}$.We want to find the probability that $x = 4$ students are singers.The formula for binomial probability is $P(X = x) = \binom{n}{x} p^x q^{n-x}$.Substituting the values: $P(X = 4) = \binom{5}{4} \left(\frac{1}{5}ight)^4 \left(\frac{4}{5}ight)^{5-4}$.$P(X = 4) = 5 	imes \left(\frac{1}{5}ight)^4 	imes \frac{4}{5}$.$P(X = 4) = 5 	imes \frac{1}{5^4} 	imes \frac{4}{5} = \frac{4}{5^4} = 4 \left(\frac{1}{5}ight)^4$.Thus,the correct option is $B$.

The probability that a student is a singer is $\frac{1}{5}$. Then,the probability that $4$ students are singers out of $5$ students is . . . . . . .

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