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

Step-by-step 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