An inspector examines items coming from an assembly line. A review of his record reveals that he accepts only 6​% of all defective items. It was also found that 2​% of all items from the assembly line are both defective and accepted by the inspector. What is the probability that a randomly chosen item from this assembly line is​ defective?

Answer 1

To find the probability that a randomly chosen item from the assembly line is defective, we can use the formula for conditional probability:

P(defective) = P(defective and accepted) + P(defective and rejected)

We are given that the inspector accepts only 6% of all defective items, so P(accepted | defective) = 0.06. We are also given that 2% of all items are both defective and accepted by the inspector, so P(defective and accepted) = 0.02.

We can now use the formula for conditional probability:

P(defective) = P(defective and accepted) / P(accepted | defective)
P(defective) = 0.02 / 0.06
P(defective) = 1/3
P(defective) = 0.333

Therefore, the probability that a randomly chosen item from this assembly line is defective is 33.3%.