A plant has three assembly lines that produce memory chips. Line one makes 50 percent of the chips and has a 4 percent defective rate. Line two produces 30 percent of the chips and has a 5 percent defective rate. Line three produces twenty percent of the chips and has a defective rate of one percent. A chip is chosen from the plant at random.
Find the probability that the chip is defective, then, given that the chip is defective, give the conditional probability for each line.