Ms. Aquina has just had a biopsy on a possibly cancerous tumor. Not wanting to spoil a week-end family event, she does not want to hear any bad news in the next few days. But if she tells the doctor to only call if the news is good, then, if the doctor does not call, Ms. Aquina can conclude that the news is bad. So, being a student of probability, Ms. Aquina instructs the doctor to flip a coin. If it comes up heads, the doctor is to call if the news is good and not to call if the news is bad. If the coin comes up tails, the doctor is not to call. In this way, even if the doctor does not call, the news is not necessarily bad. Let C = {the tumor is cancerous} and N = {the doctor does not call}. Let = P(C) and = P(C|N). Assume the coin is fair. (a) Find in terms of (b) Show that with equality if and only if = 0 or = 1.