Please perform all calculations using 4 significant figures (or fractions), and report all answering using 4 significant figures.

Say you are a petroleum geologist, and you have a seismic test for underground oil reservoirs. This test has a false positive rate of 0.2 (i.e., a 20% chance of testing positive when there is no oil) and a false negative rate of 0.1 (i.e., a 10% chance of testing negative when there is oil). Ten percent of fields that are geologically similar to the one you are currently testing prove to have significant underground oil reservoirs. (a) What is the probability that there is oil under this field if it tests positive? (b) What is the probability that there is oil if it tests negative?