A leukemia patient is being treated with a combination of three drugs: drug A, drug B, drug C. It has been observed that when all three are used simultaneously, often two of the three drugs will be inhibited so that only one will be actively fighting the tumor. Assume that when this occurs the probability that drug A is acting alone is the same as that for drug B and drug C, or 1/3.

The effectiveness of each drug alone in producing remission is different. Drug A has been observed to be effective 30% of the time, drug B 55% of the time and drug C 40% of the time. Suppose that the three drugs are used in combination and only one is actively fighting the tumor. The patient has gone into remission. What is the probability that drug B alone was responsible for the remission?