A valve can be used at four temperature levels If the valve

A valve can be used at four temperature levels. If the valve is used at the cold temperature, then there is a probability of 0.003 that it will leak. If the valve is used at the 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 0.018 that it will leak. If the valve is used at hot temperature, then there is a probability of 0.014 that it will leak. Under standard operating conditions, the valve is used at a clod temperature 12% of the time, at a medium temperature 55% of the time, at warm temperature 20% of the time, and at hot temperature 13% of the time.

A) If the value leaks, what is the probability that it is being used at the hot temperature?

Solution

Let A be the probability that the valve leaks

B it is used at the hot temperature.

Required probability = P(A/B) = conditional prob

Refer conditional prob formula

P(A/B) =  = =0.1076