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.

a. What is the probability that a randomly selected household uses heating oil?
b. What is the probability that a randomly selected household is delinquent in paying its utility bill?
c. What is the probability that a randomly selected household uses heating oil and is delinquent in paying its utility bill?
d. Given that a household uses heating oil, what is the probability that it is delinquent in paying its utility bill?
e. Given that a household is delinquent in paying its utility bill, what is the probability that the household uses electricity?
f. Are the events €œHeating Oil€ and €œDelinquent in Payment€ independent? Explain usingprobabilities.

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Type of Heating Delinquent Natural in Payment? Gas Electricity Oil Propane Heating Yes No 0 50 20 130 15 10 240 20 15