MATH 350 Homework 08
Due at the end of class on 2024-04-19
- A factory produces electrical components using two machines: Machine X and Machine Y. On any given day, Machine X produces 60% of the total output, while Machine Y produces the remaining 40%. It is known that 5% of the components produced by Machine X are defective, whereas only 2% of the components produced by Machine Y are defective. If a randomly selected component is found to be defective, what is the conditional probability that it was produced by Machine X?
- In a factory, two machines, A and B, are used to produce a
specific part. Machine A produces 70% of the parts, and
Machine B produces the remaining 30%. However, 5% of the
parts from Machine A and 3% of the parts from Machine B are
defective. An inspector randomly selects a part and finds it
to be defective.
- What is the probability that this defective part was produced by Machine A?
- If another part is randomly selected and it's not defective, what is the probability that it was produced by Machine B?