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 not a swimmer,so $p = \frac{1}{5}$.Let $q$ be the probability that a student is a swimmer,so $q = 1 -

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 not a swimmer,so $p = \frac{1}{5}$.Let $q$ be the probability that a student is a swimmer,so $q = 1 - p = 1 - \frac{1}{5} = \frac{4}{5}$.We need to find the probability that out of $n = 5$ students,$k = 4$ are swimmers.Using the binomial distribution formula $P(X = k) = {}^nC_k \cdot q^k \cdot p^{n-k}$,we have:$P(X = 4) = {}^5C_4 \cdot \left( \frac{4}{5} \right)^4 \cdot \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 $\frac{1}{5}$. What is the probability that out of $5$ students,$4$ are swimmers?

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