31. A frictionless pulley system, which lifts a box, is shown in the figure. The weight of the box follows a normal distribution . The resistances of the two cables follow distributions and . Determine the probabilities of failure of the cables. are independently distributed.

Solution

From the figure, we have

Then we construct the functions

From which, we have

Thus, the probabilities of failure of cable 1 and cable 2 are

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