The probability that a student is not a swimm | vedclass

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(D) 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 =

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None of these

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(D) 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 need to find the probability that out of $n = 5$ students,$x = 4$ are swimmers.Using the Binomial Distribution formula: $P(X = x) = ^nC_x \cdot p^x \cdot q^{n-x}$.Substituting the values: $P(X = 4) = ^5C_4 \cdot \left(\frac{4}{5}\right)^4 \cdot \left(\frac{1}{5}\right)^{5-4}$.$P(X = 4) = 5 \cdot \left(\frac{4}{5}\right)^4 \cdot \frac{1}{5} = \left(\frac{4}{5}\right)^4$.Since this value is not explicitly listed in the options $A, B, C$,the correct choice is $D$.

The probability that a student is not a swimmer is $\frac{1}{5}$. Then,the probability that out of $5$ students,$4$ are swimmers is . . . . . . .

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