Answer: c. 0.0778
Step-by-step explanation:
Let X is the number of non-authentic names in her sample with parameter :
n= 5 and p=40% = 0.40
Binomial probability distribution, the probability of getting success in x trials :-
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]
We have ,
[tex]P(X=0)=^{5}C_0(0.40)^0(1-0.40)^{5}\\\\=(1)(0.60)^{5}\\\\=0.07776\approx0.0778[/tex]
Thus , the correct answer is option c. 0.0778