Question

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

Answer:

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

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

Step-by-step 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.  

We get:

$P=\frac{6}{40}\cdot \frac{5}{39}\\\\P=\frac{1}{52}$

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.  

We get:

$P=\frac{6}{40}\cdot \frac{6}{40}\\\\P=\frac{9}{400}$

Therefore, the probability is P=9/400.