Question

question 8
3 pts
in the 2019 status of energy report issued by the nevada governors office of energy, 89% of the electricity in the state of nevada is provided by nv energy. two nevada homes are selected at random. assuming that the source of energy to each home in nevada is independent of the source of energy to another home in the state (enter your answers below without rounding them):
a) what is the probability that both homes purchase their electricity from nv energy?
b) what is the probability that at least one of the homes purchases its needed electricity from nv energy?
c) what is the probability that neither home purchases its needed electricity from nv energy?

Explanation:

Step1: Define probabilities

Let \( P(A) = 0.89\) (probability a home gets electricity from NV Energy). Since events are independent.

Step2: Solve part (a)

For two independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\). Here \(P(A) = P(B)=0.89\), so \(P = 0.89\times0.89=0.7921\)

Step3: Solve part (c)

The probability that a home does not get electricity from NV Energy is \(1 - 0.89=0.11\). For two independent homes, \(P(\text{neither})=(1 - 0.89)\times(1 - 0.89)=0.11\times0.11 = 0.0121\)

Step4: Solve part (b)

Use the formula \(P(\text{at least one})=1 - P(\text{neither})\). Since \(P(\text{neither}) = 0.0121\), then \(P(\text{at least one})=1-0.0121 = 0.9879\)

Answer:

a) \(0.7921\)
b) \(0.9879\)
c) \(0.0121\)