The probability that a student is not a swimmer is $\cfrac{1}{5}$ . Then the probability that out of five students, four are swimmer is

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

(B) ${\left( {\cfrac{4}{5}} \right)^4}\cfrac{1}{5}$

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

(D) None of these

Option A is correct

$p$ , the probability that the student is not a swimmer $= \cfrac{1}{5}$

$\Rightarrow$ $q = 1 - p = 1 - \cfrac{1}{5} = \cfrac{4}{5}$ and $n = 5$

$$\therefore $$ $P(X = 4){ = ^5}{C_4}{q^1}{p^4}{ = ^5}{C_4}{\left( {\cfrac{4}{5}} \right)^4}\left( {\cfrac{1}{5}} \right) = 5{\left( {\cfrac{4}{5}} \right)^4}\left( {\cfrac{1}{5}} \right) = {\left( {\cfrac{4}{5}} \right)^4}$

Miscellaneous Exercise