Question

The probability that a student is not a swimmer is $1/5$. The probability that out of $5$ students exactly $4$ are swimmer is

• A. ${\left(\frac{4}{5}\right)}^3$
• B. ${\left(\frac{4}{5}\right)}^4$
• C. $5{\left(\frac{4}{5}\right)}^4$
• D. $3{\left(\frac{4}{5}\right)}^3$

Answer 1

Answer: (B)

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

Let $p=$ probability that a student selected at random is a swimmer $=1-1/5=4/5$
$n=$ number of students selected $=5$
and $X=$ number of swimmers
Then $XB(n,p)$ where $n=5$ and $p=4/5$
Probability that exactly 4 students are swimmer is
${=}^5{C}_4{p}^{4}q=5{\left(\frac{4}{5}\right)}^4\left(\frac{1}{5}\right)={\left(\frac{4}{5}\right)}^4$.