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. ${}^5{C}_4{\left(\frac{4}{5}\right)}^4\frac{1}{5}$
• B. ${\left(\frac{4}{5}\right)}^4\frac{1}{5}$
• C. ${}^5{C}_1\frac{1}{5}{\left(\frac{4}{5}\right)}^4$
• D. none of these.

Answer 1

Answer: (C)

${}^5{C}_1\frac{1}{5}{\left(\frac{4}{5}\right)}^4$

Here $p=\frac{4}{5},n=5,q=1-p=\frac{1}{5}$
Hence required probability is ${=}^5{C}_4\left(\frac{1}{5}\right){\left(\frac{4}{5}\right)}^4{=}^5{C}_1\left(\frac{1}{5}\right){\left(\frac{4}{5}\right)}^4$