Question

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

• A. ${}^5{C}_4\left(\frac{4}{5}{)}^2\right(\frac{1}{2})$
• B. $\left(\frac{4}{5}{)}^4\right(\frac{1}{5})$
• C. ${}^5{C}_1\left(\frac{1}{5}\right)(\frac{4}{5}{)}^4$
• D. None of these

Answer 1

Answer: (C)

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

Here $q=p$ (not swimmer ) $=\frac{1}{5}$
$\therefore =p$(swimmer) $=1-q$
$=1-\frac{1}{5}=\frac{4}{5}$
$\therefore$ Required probability ${=}^5{C}_4{p}^4{q}^{5-4}$
${=}^5{C}_1\left(\frac{4}{5}{)}^4\right(\frac{1}{5}{)}^1$
${=}^5{C}_1\left(\frac{1}{5}\right)(\frac{4}{5}{)}^4$