The probability that a student is not a swimm | vedclass

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Question

(A) Let $p$ be the probability that a student is a swimmer and $q$ be the probability that a student is not a swimmer. Given $q = \frac{1}{5}$,so $p =

Vedclass · Accepted Answer

$5 	imes (\frac{4}{5})^4 	imes \frac{1}{5}$

Vedclass · Answer

(A) Let $p$ be the probability that a student is a swimmer and $q$ be the probability that a student is not a swimmer. Given $q = \frac{1}{5}$,so $p = 1 - q = 1 - \frac{1}{5} = \frac{4}{5}$. We have $n = 5$ students and we want to find the probability that $x = 4$ are swimmers. Using the Binomial distribution formula $P(X = x) = ^nC_x \cdot p^x \cdot q^{n-x}$: $P(X = 4) = ^5C_4 \cdot (\frac{4}{5})^4 \cdot (\frac{1}{5})^{5-4}$ $P(X = 4) = 5 \cdot (\frac{4}{5})^4 \cdot \frac{1}{5}$ $P(X = 4) = (\frac{4}{5})^4$ However,looking at the provided options,the expression $5 	imes (\frac{4}{5})^4 	imes \frac{1}{5}$ simplifies to $(\frac{4}{5})^4$. Since this is not explicitly listed as a simplified value,we select the form that matches the binomial expansion structure.

The probability that a student is not a swimmer is $\frac{1}{5}$. The probability that out of $5$ students selected at random,$4$ are swimmers is:

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