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(B) Let $n = 5$ be the total number of students. Let $p$ be the probability that a student is a swimmer. Given that the probability that a student is

Vedclass · Accepted Answer

$^5C_1 \left( \frac{4}{5} \right) \left( \frac{1}{5} \right)^4$

Vedclass · Answer

(B) Let $n = 5$ be the total number of students. Let $p$ be the probability that a student is a swimmer. Given that the probability that a student is not a swimmer is $\frac{1}{5}$,we have $q = \frac{1}{5}$. Therefore,$p = 1 - q = 1 - \frac{1}{5} = \frac{4}{5}$. Using the binomial distribution formula $P(X = r) = {}^nC_r p^r q^{n-r}$,where $r = 1$ is the number of swimmers. $P(X = 1) = {}^5C_1 \left( \frac{4}{5} \right)^1 \left( \frac{1}{5} \right)^{5-1} = {}^5C_1 \left( \frac{4}{5} \right) \left( \frac{1}{5} \right)^4$. Thus,the correct option is $B$.

If the probability that a student is not a swimmer is $\frac{1}{5}$,then the probability that out of $5$ students one is a swimmer is

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