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.
Answer: 0.9919
Step-by-step explanation:
Binomial probability formula :-
[tex]P(x)=^nC_xp^x\ (1-p)^{n-x}[/tex], where n is total number of trials , P(x) is the probability of getting success in x trials and p is the probability of getting success in each trial.
Given : The proportion of the people have been vaccinated: p=0.7
If 4 people are randomly selected, then the probability that at least one of them has been vaccinated will be :-
[tex]P(X\geq1)=1-P(0)[/tex]
[tex]=1-^4^C_0(0.7)^0(0.3)^4\\\\=1-(0.3)^4=0.9919[/tex]
Hence, the probability that at least one of them has been vaccinated =0.9919
