More and more households are struggling to pay utility bills given a shaky economy and high heating costs (The Wall Street Journal, February 14, 2008). Particularly hard hit are households with homes heated with propane or heating oil. Many of these households are spending twice as much to stay warm this winter compared to those who heat with natural gas or electricity. A representative sample of 500 households was taken to investigate if the type of heating influences whether or not a household is delinquent in paying its utility bill. The following table reports the results.

Delinquent in Payment?	Type of Heating
Natural Gas	Electricity	Heating Oil	Propane
Yes	50	20	15	10
No	240	130	20	15

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a.	What is the probability that a randomly selected household uses heating oil? (Round your answer to 2 decimal places.)

Probability

b.	What is the probability that a randomly selected household is delinquent in paying its utility bill? (Round your answer to 2 decimal places.)

Probability

c.	What is the probability that a randomly selected household uses heating oil and is delinquent in paying its utility bill? (Round your answer to 2 decimal places.)

Probability

d.	Given that a household uses heating oil, what is the probability that it is delinquent in paying its utility bill? (Round your intermediate calculations and final answer to 4 decimal places)

Probability

e.	Given that a household is delinquent in paying its utility bill, what is the probability that the household uses electricity? (Round your intermediate calculations and final answer to 4 decimal places)

Probability

f.	Are the events Heating Oil and Delinquent in Payment independent?
	Yes because P(Yes | Heating Oil) = P(Yes). Yes because P(Yes Heating Oil) = P(Yes). No because P(Yes | Heating Oil) P(Yes).