We know that, in Suburbia, the type of heating fuel used and the type of air con

Question

We know that, in Suburbia, the type of heating fuel used and the type of air conditioning used are statistically independent random variables in single family homes. These probability distributions are given below: Fuel System Heating Oil Natural Gas Total Probability .30 .70 1.00 Iype ol Air Conditioning Central Air Window units No A/C Total Probability .70 .20 .10 1.00 a. b. c. Find the probability a randomly selected house has natural gas and central air If a specific home has natural gas, what is the probability this home has central air? What is the probability a randomly selected home has central air or natural gas?

Explanation / Answer

Since the events are independent:

a) P(Natural gas and Central air) = P(Natural gas)*P(Central air) = 0.70*0.70 = 0.49

b) P(Central air | Natural gas) = P(Central air) = 0.70

c) P(Central air or natural gas) = 0.70 + 0.70 - 0.49 = 0.91

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