The probability that a student is not a swimmer is 1 / 5. Then the probability that out of five students, four are swimmers is
A. { }^{5} \mathrm{C}{4} 1 / 5(4 / 5)^{4}
B. (4 / 5)^{4}(1 / 5)
C. { }^{5} \mathrm{C}{1} 1 / 5(4 / 5)^{4}
D. None of these
The probability that a student is not a swimmer is 1 / 5. Then the probability that out of five students, four are swimmers is
A. { }^{5} \mathrm{C}{4} 1 / 5(4 / 5)^{4}
B. (4 / 5)^{4}(1 / 5)
C. { }^{5} \mathrm{C}{1} 1 / 5(4 / 5)^{4}
D. None of these

Solution:
Answer: A. { }^{5} \mathrm{C}_{4} 1 / 5(4 / 5)^{4}

Explanation:

Assume that X is the number of pupils who are swimmers out of a class of five. The Bernoulli trials are also used to select students who are swimmers on a regular basis. As a result, the likelihood of kids who are not swimmers =\mathrm{q}=1 / 5

Clearly, we have \mathrm{X} has the binomial distribution where \mathrm{n}=5

And, p=1-q

=1-1 / 5

=4 / 5

\therefore P(X=x)={ }^{n} C_{x} q^{n-x} p^{x}

={ }^{5} C_{x}\left(\frac{1}{5}\right)^{5-x} \cdot\left(\frac{4}{5}\right)^{x}

Hence, probability that four students are swimmers =\mathrm{P}(\mathrm{X}=4)
={ }^{5} C_{4}\left(\frac{1}{5}\right) \cdot\left(\frac{4}{5}\right)^{4}

\therefore Option A is correct