A lot of 100 semiconductor chips contains 20 chips that are

A lot of 100 semiconductor chips contains 20 chips that are defective. Three chips are selected randomly, WITH REPLACEMENT, from the lot.

1) What is the probability that the second one selected is defective given that the first one was defective?

2) What is the probability that both the first and second chips selected were defective?

3) What is the probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay

4) What is the probability that all three are defective?

please explain as briefly how to solve

Solution

(1)

Since chips are selected with replacement so for each selection probability that chip will be defective remain same. So the probability that the second one selected is defective given that the first one was defective will be 20/100 = 0.2.

(2)

Since selection are independent from each other so the probability that both the first and second chips selected were defective is (20/100)*(20/100) = 0.04.

(3)

The probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay will be

(20/100)* (80/100)*(20/100) = 0.032

(4)

The probability that all three are defective is

(20/100)* (20/100)*(20/100) = 0.008