21. Plate AB is used to hold the ball. If the weight of the ball W and the applied force P exerted on the plate are independently and normally distributed with W ~ N(4, 0.05²) kg and P ~ N(55, 0.5²) N, respectively, determine the probability that the ball will fall. The wall is assuming to be smooth.

Solution

According to the force equilibrium on the ball, we have

Thus, we could obtain

The probability that the ball might fall is

Then, we may construct Y as below and the probability constraint becomes

Therefore, we have

Consequently, the probability the ball might fall is

Ans.