3. a) In Arlington, 25% of all homes are all electric. Sixty percent of the all electric homes have air conditioning while only one-fourth of the gas-heated homes are air-conditioned. During a casual conversation, a young woman you just met at Bardo remarks how nice it is to return home after work this summer because her air-conditioning is set very low. What is the probability that she lives in an all electric home?
b) You are the production manager for ING Oil and Gas Exploration examining a candidate site. Assume that oil either exists in producible quantities or does not exist at all. Similar site have yielded oil about 20% of the time.
A test is performed on the soil at the site. In the past, oil was present 90% of the times that the test indicated "oil." Conversely, oil was actually present 15% when the test results indicated "no oil."
If a single test is run and indicates that oil is present,what is the revised probability that oil is actually present.