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 $q = 1/5$,so $p = 1 - 1/5

Vedclass · Accepted Answer

$^5C_4 \left( \frac{4}{5} \right)^4 \left( \frac{1}{5} \right)$

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 $q = 1/5$,so $p = 1 - 1/5 = 4/5$.Using the binomial distribution formula $P(X = k) = ^nC_k p^k q^{n-k}$,where $n = 5$ and $k = 4$:$P(X = 4) = ^5C_4 \left( \frac{4}{5} \right)^4 \left( \frac{1}{5} \right)^{5-4}$$P(X = 4) = ^5C_4 \left( \frac{4}{5} \right)^4 \left( \frac{1}{5} \right)$

The probability that a student is not a swimmer is $1/5$. What is the probability that $4$ out of $5$ students are swimmers?

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