Covid-19

Data showed that 22% of people in a small town were infected with the COVID-19 virus. A random sample of six
residents from this town was selected. Find the probability that exactly two of these residents were infected.

Correct answer:

p =  26.8729 %

Step-by-step explanation:

$$\begin{gathered} q=22\%=\frac{22}{100}=\frac{11}{50}=0.22 \\ {C}_2(6)=\left(\genfrac{}{}{0ex}{}{6}{2}\right)=\frac{6!}{2!(6-2)!}=\frac{6\cdot 5}{2\cdot 1}=15 \\ p=100\cdot \left(\genfrac{}{}{0ex}{}{6}{2}\right)\cdot q^2\cdot (1-q{)}^4=100\cdot 15\cdot 0.22^2\cdot (1-0.22{)}^4=26.8729\% \end{gathered}$$

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