A valve can be used at four temperature levels. If the valve is used at a cold temperature, then there is a probability of 0.003 that it will leak. If the valve is used at a medium temperature, then there is a probability of 0.009 that it will leak. If the valve is used at a warm temperature, then there is a probability of 0.014 that it will leak. If the valve is used at a hot temperature, then there is a probability of 0.0 IS that it will leak. Under standard operating conditions, the valve is used at a cold temperature 12% of the time, at a medium temperature 55% of the time, at a warm temperature 20% of the time, and at a hot temperature 13% of the time,
(a) If the valve leaks, what is the probability that it is being used at the hot temperature?
(b) If the valve does not leak, what is the probability that it is being used at the medium temperature?