Answer: 0.064
Step-by-step explanation:
Binomial probability formula :-
[tex]P(X)=^nC_x \ p^x\ (1-p)^{n-x}[/tex], where P(x) is the probability of getting success in x trials, n is total number of trials and p is the probability of getting succes in each trial.
Given : The proportion of the homes constructed in the Quail Creek area include a security system : [tex]p=0.40[/tex]
Now, if three homes are selected at random, then the probability all three of the selected homes have a security system is given by :-
[tex]P(3)=^3C_3 \ (0.40)^3\ (1-0.40)^{3-3}\\\\=(0.40)^3=0.064[/tex]
Hence, the probability all three of the selected homes have a security system = 0.064
