1. In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

## If the bag is defective, what is the probability that it came from line 1?

1. Two production lines are used to pack sugar into 5 kg bags. Line 1 produces twice as many bags as does line 2. One percent of the bags from line 1 are defective in that they fail to meet a purity specification, while 3% of the bags from line 2 are defective. A bag is randomly chosen for inspection.

a. What is the probability that it came from line 1?

b. What is the probability that it is defective?

c. If the bag is defective, what is the probability that it came from line 1?

d. If the bag is not defective, what is the probability that it came from line 1?

2. Four bricks are sampled from a large load and the crushing strength of each is measured to determine whether it meets a specification. If any of the four fail to meet the specification, the load will be returned. If in fact 10% of the bricks in the load fail to meet the specification, what is the probability that the load will be returned?