Three machines A, B, and C—are used to produce a large quantity of identical parts at a factory.

Question

Three machines A, B, and C—are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machines B and C produce 30% and 10% of the parts, respectively. Historical records indicate that 3% of the parts produced by Machine A are defective, compared with 2%for Machine B, and 1% for Machine C.

1. what is the probability that you will receive a part from machine B and that it will NOT be defective?
2. what is the probability that you will receive a defective part?
3. given a part is defective, what is the probability that it was from machine A?

Answer 1

1) P(-D/B)= 100%-2%

= 98%

2) P(D)=.6(3)+.3(2)+.1(1)=1.8+.6+.1

= 2.5%

3) P(A/D)=1.8/2.5= 18/25= 72%