Question

Instruction: The following questions need you show all your work in details. Question 3. (5 points) A machine produces defective parts with three different probabilities depending on its state of repair. If the machine is in good working order, it produces defective parts with probability 0.02. If it is wearing down, it produces defective parts with probability 0.1. If it needs maintenance, it produces defective parts with probability 0.3. The probability that the machine is in good working order is 0.8, the probability that it is wearing down is 0 .1, and the probability that it needs maintenance is 0.1. Compute the probability that a randomly selected part will be defective.

Answer 1

$Let~A~be~an~event~that~the~machine~is~in~good~working~order,\\ B~be~an~event~that~the~machine~is~wearing~down,\\ C~be~an~event~that~machine~needs~maintenance\\ Here,~P(A)=0.8,~P(B)=0.1,~P(C)=0.1\\ Let~D~be~an~event~of~selecting~defective~part.\\ Here,~P(D|A)=0.02,~P(D|B)=0.1,~P(D|C)=0.3\\ Required~probability=P(D)=P(D|A)P(D)+P(D|B)P(D)+P(D|C)P(D)\\ =0.02*0.8+0.1*0.1+0.3*0.1=0.056$