Answer: 0.0542438
Step-by-step explanation:
Given : The proportion of newly formed companies in 2010 appeared to have outstanding prospects : [tex]p=\dfrac{11}{400}=0.0275[/tex]
The number of companies selected : n=2
Using the binomial distribution, the probability of getting success in x trials :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where n is the total number of trials and p is the probability of getting success in each trial.
Then , the probability that at least one of the investor's companies had outstanding prospects :-
[tex]P(x\geq1)=1-P(0)=1-^{2}C_0(0.0275)^0(1-0.0275)^2\\\\=1-(0.9725)^2=0.05424375\approx0.0542438[/tex]
Hence, the probability that at least one of the investor's companies had outstanding prospects = 0.0542438
