Question

can you help me solve this problem?Data showed that 27% of people in a small town was infected with the COVID-19 virus. A random sample of nine resident from this town was selected. Find the probability that at least three of these residents will be infected.i need 4 digit decimals answer.

Answer 1

`\begin{gathered} \text{Given} \\ P(\text{Infected})=0.27\text{ from 27\% infection} \end{gathered}`
`\begin{gathered} \text{It is much easier to calculate the probability of the complement (getting 3 infected),} \\ \text{and subtracting from }1 \\ \\ P(at\text{ least 3 infected})=1-P(\text{exactly 3 are infected}) \\ P(at\text{ least 3 infected})=1-(0.27)^3 \\ P(at\text{ least 3 infected})=0.980317 \end{gathered}`

Rounding off to 4 decimals, the probability is 0.9803.