28. Two independently normally distributed weight m~ N(10, 0.5²) kg and force P ~ N(100, 1.5²) N are shown in the system. If the cable AB is in the position shown below, determine the probability that the system may fail if the allowable tension of AB is 85 N.

Solution

Solve the above equations, we have

Therefore, we have

The maximum tension of cable AB is 80 N, thus the probability that the system might fail is, where

Finally, the probability is

Ans.