In a large population, 70 % of the people have been vaccinated. If 4 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Accepted Solution
A:
Answer:The probability that at least one of the 4 people has been vaccinated is 0.9919.Step-by-step explanation:It is given that in a large population, 70 % of the people have been vaccinated. So, the probability of success is[tex]p=\frac{70}{100}=0.7[/tex]Probability of failure is[tex]q=1-p=1-0.7[/tex]According to binomial distribution.[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]We need to find the probability that at least one of the 4 people has been vaccinated.[tex]P(x\geq 1)=1-P(x<1)[/tex][tex]P(x\geq 1)=1-P(x=1)[/tex][tex]P=1-^4C_0(0.7)^0(0.3)^{4-0}[/tex][tex]P=1-1(0.0081)[/tex][tex]P=0.9919[/tex]Therefore the probability that at least one of the 4 people has been vaccinated is 0.9919.