Suppose a lot of machine parts are delivered, where a part i…

Suppose a lot of machine parts are delivered, where a part is considered acceptable only if it passes tolerance. We check these parts until we find 1 part doesn’t satisfy the tolerance. From experience, the acceptance rate of each part is 0.8. What is the probability of this event, if we checked 10 parts until we got 1 part which didn’t pass ? (You may use a distribution to compute it)  

A company uses a special screw. The company gets screws from…

A company uses a special screw. The company gets screws from three different Manufacturers. If a screw is defective, it will cause damage in production in company. (Note, that the third column in table has conditional probabilities.)   What the probability of the joint event: a defective screw is made by Manufacturer B. If a screw is found to be defective, what is the probability that it came from Manufacturer C.