Question

In a group of 30 ballpoint pens on a shelf in the stationery department of Metro Department Store, 2 are known to be defective. (Round your answers to three decimal places.) (a) If a customer selects 3 of these pens, what is the probability that at least 1 is defective? (b) If a customer selects 3 of these pens, what is the probability that no more than 1 is defective?

Answer 1

To find the probability that at least 1 of the 3 pens selected by a customer is defective, we subtract the probability of none of the pens being defective from 1.

Step-by-step explanation:

To find the probability that at least 1 of the 3 pens selected by a customer is defective, we need to find the probability that none of the pens is defective and subtract that from 1.

In a group of 30 pens, 2 are defective and 28 are not defective. So the probability of selecting a pen that is not defective is 28/30 for the first pick, 27/29 for the second pick, and 26/28 for the third pick.

Therefore, the probability that none of the pens is defective is (28/30) * (27/29) * (26/28) = 0.794.

So the probability that at least 1 of the pens is defective is 1 - 0.794 = 0.206.