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.

1) If the valve does not leak, what is the probability that it is being used at the medium temperature?

Solution

https://gm1.ggpht.com/Vn6c89vkiSz8yX9bPdtqPU-zs5fDz_AXLsnGMvP5nZpbFX8TjHS7WzXN2feipT13wZ9ei-RgeHEDYnOm-FmFZKVrhRXdfqyYOli7ULsYJJg3gJYgX7SMmQ7sVxTWQExqfN1jV-YZiePT59RytNse2_N4oDvfVNRTyVR2WVTGoDLM5B5sFPR_UnbOWEGrM8NU39-5cSDZqIDc4XQdtPOXROPpfcXSuB2kJbIIt9Ith-KzR72wY2CGrP-teBtBF8LyCTsF_pUmmV7ITFiYr3oFTKSIOkzpdS17JEwafqJ3G_n_H9jIVKRwlK-acXjoeRbgP5POpVQOIHpsORN_Gmd3cIzcVFlE6o-e7J-EdZzf2KZmeFeQ1KmfI9aNl-ccbWIfDZscaOMzoAZ7n0ZDk475YXq2mvBWFvwCSjSLNxm_V3K-CLkHwkl3zrfHgwJ8uapSKL8pnlIHDSDxQfqRm8OiUDI10xN12ax7TrFDnyMUqtbo18U3ikdBxu8Ba0nyxUT2Y5R9uATxnGMQZtKO5OUmEnJ1dK5MgbjY2Pdf395ko81Q0sVYNdOjmg4Uh283mTD5z39tYsOk=w1338-h506-l75-ft