Question

The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students, four are swimmers is
(A)$\ ^5 C_4\biggr\lgroup\frac{4}{5}\biggr\rgroup ^4 \frac15$
(B)$\biggr\lgroup\frac{4}{5}\biggr\rgroup ^4 \frac15$
(C)$\ ^5 C_1 \frac15 \biggr\lgroup\frac{1}{5}\biggr\rgroup ^4$
(D)None of these

Answer 1

Let

X: be number of swimmers

Picking a student is a Bernoulli trial

So,X has binomial distribution

P(X=x)=nC×Qn-xPx