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3 years ago

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Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: Wh

at is the probability all three of the selected homes have a security system

1 answer:

suter [353]3 years ago

6 0

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

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