Question

In an assembly-line operation, 1/3 of the items being produced are defective. If three items are picked at random and tested, what is the probability that (a) that exactly one of them will be defective and (b) that at least one of them will be defective.

Answer 1

Answer:

(a) 4/9 (b) 19/27

Step-by-step explanation:

P(defective) = 1/3 (Given)

Find the probability that it is not defective:

P(Not defective) = 1 - 1/3 = 2/3

(a) Find the probability that exactly one of the three items picked are defective:

P(one out of 3 is defective) = 3 (1/3)(2/3)(2/3) = 4/9

(b) Find the probability that at least one of the three items picked are defective:

P(at least one is defective) = 1 - P(none is defective)

P(at least one is defective) = 1 - (2/3)(2/3)(2/3) = 19/27

Answer: (a) 4/9 (b) 19/27