Question

Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: What is the probability all three of the selected homes have a security system

Answer 1

Answer: 0.064

Explanation:

Binomial probability formula :-

`P(X)=^nC_x \ p^x\ (1-p)^(n-x)`, 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 :
`p=0.40`

Now, if three homes are selected at random, then the probability all three of the selected homes have a security system is given by :-

`P(3)=^3C_3 \ (0.40)^3\ (1-0.40)^(3-3)\\\\=(0.40)^3=0.064`

Hence, the probability all three of the selected homes have a security system = 0.064