Zany probablity problem.....
A lady had a biopsy on a possibly cancerous tumor. She instructs the doctor to flip a coin. If it comes up heads, will call if the news is good but not if it is bad. If it comes up tails, the doctor will not call no matter what the results are. Let a be the probability that the tumor is cancerous and b the conditional probability that the tumor is cancerous given the doctor does not call.
Find b in terms of a and determine which probability is larger.
Intuition tells me the probability of b is the larger of the two, but I don't know how to show this.