An electronic device is operated under three temperature settings of low, medium, and high (i.e., L, M, H) and two vibration conditions of V1 and V2. The reliability of the device depends on the temperature and vibration conditions of operation. Define a partition of the sample space of operation.

Assume that the device is equally likely to be in any of these conditions, and that the failure probabilities (Pf) corresponding to combinations of these conditions are Pf(L,V1) = Pf(M,V1) = 0.05, Pf(L,V2) = Pf(M,V2) = 0.10, Pf(H,V1) = 0.20, and Pf(H,V2) = 0.15. Compute the failure probability of the device. What is its reliability? For a particular device that has failed, what is the probability that it was operated in (H,V1)? in (M,V2)?