The probability that a student is not a swimm | vedclass

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Question

(A) The selection of students who are swimmers follows a binomial distribution. Let $X$ be the number of students who are swimmers out of $n=5$ studen

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The selection of students who are swimmers follows a binomial distribution. Let $X$ be the number of students who are swimmers out of $n=5$ students.The probability that a student is not a swimmer is $q = \frac{1}{5}$.The probability that a student is a swimmer is $p = 1 - q = 1 - \frac{1}{5} = \frac{4}{5}$.The probability distribution is given by $P(X=x) = ^{n}C_{x} p^{x} q^{n-x}$.For $n=5$ and $x=4$,we have:$P(X=4) = ^{5}C_{4} \left(\frac{4}{5}\right)^{4} \left(\frac{1}{5}\right)^{5-4} = ^{5}C_{4} \left(\frac{4}{5}\right)^{4} \left(\frac{1}{5}\right)$.Thus,the correct option is $A$.

The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students,four are swimmers is

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