Question

There are two injection molding machines that produce plastic game pieces. Recently, burn marks have been a quality issue for this product. Mold machine A produces 40% of the total output of game pieces. The probability that a burn mark is detected at final inspection given that the game piece was manufactured on Machine A is equal to 0.08. The burn mark rate given that a game piece is made by Machine B is equal to 0.02.

• Find the probability that a game piece has a burn mark given that it is from Machine A.

• Find the probability that a randomly chosen game piece has a burn mark and is from Machine B.

• A burn mark is found on a game piece during final inspection. What is the probability that it was produced by Machine B?

Answer 1

Define the events

Also A and B are complementary events. .

The following probabilities are given.

Using total probability theorem,

The probability that a game piece has a burn mark given that it is from Machine A

The probability that a randomly chosen game piece has a burn mark and is from Machine B

The conditional probability,