After your yearly checkup, the doctor has good news and bad news. The bad news is that you tested positive for a serious disease and that the test is very accurate: the probability of testing positive when you do have the disease is 0.983, and the probability of testing negative when you don't have the disease is 0.945. The good news is that this is a rare disease, striking only one in ten thousand people in your demographic.

Now assign a cost to the errors: deciding to seek treatment for the cancer when in fact you are healthy will cost you $1000 in unnecessary tests and the recovery therefrom. Deciding to forgo treatment when in fact you have the cancer will cost you and your family $1,000,000 in loss of life/income etc. Assume a correct decision (seek treatment if you have cancer, forgo treatment if you are healthy) has no cost, for simplicity.

(i) What is the expected cost (i.e., "risk") assuming the cancer test comes out positive and you undergo treatment?

(ii) What should your decision be after a positive test, in light of the expected costs? (Is this different from the answer to part (a)?)

(iii) What is the expected cost if the cancer test is negative and you do not undergo treatment?