Question

In a bicycle manufacturing factory, manufacturing manager is concerned about a possible defective of their product. If there were a defective, there is a probability of 0.20 of a defect in the brake, 0.23 of a defect in the tire, 0.15 of a defect in the pedal, and 0.42 of a defect in the body frame. (a) What is the probability that the defective occurred from the brake or the body frame if the defects can be caused from both simultaneously in the probability of 0.05? (b) What is the probability that there are no defects in either brake or the body frame?

Answer 1

Let A be the event of defect in brake , B be the defect in the body frame

P(A) = .2; P(B)=.42,P(A and B) = .05

A)P(A or B)= P(A)+P(B)- P(A and B) =.2+.42-.05 = .57

B) P(neither A nor B)= 1- P(A or B)= 1- .57 = .43