Question

a. A batch of 40 parts contains six defects. If two parts are drawn randomly one at a time without replacement, what is the probability that both parts are defective? b. If this experiment is repeated, with replacement, what is the probability that both parts are defective?

Answer 1

a) Therefore, the probability is P=1/52.

b) Therefore, the probability is P=9/400.

Explanation:

We know that a batch of 40 parts contains six defects.

a) We calculate the probability that the both parts are defective, if two parts are drawn randomly one at a time without replacement.

The probability for the first is 6/40.

The probability for the second is 5/39.

Therefore, we get

`P=(6)/(40)\cdot (5)/(39)\\\\P=(1)/(52)\\`

Therefore, the probability is P=1/52.

b) We calculate the probability that the both parts are defective, if two parts are drawn randomly one at a time with replacement.

The probability for the first is 6/40.

The probability for the second is 6/40.

Therefore, we get

`P=(6)/(40)\cdot (6)/(40)\\\\P=(9)/(400)\\`

Therefore, the probability is P=9/400.