Question

Suppose that ten items are chosen at random from a large batch delivered to a company. The manufacturer claims that just 3% of the items in the batch are defective. Assume that the batch is large enough so that even though the selection is made without replacement, the number 0.03 can be used to approximate the probability that any one of the ten items is defective. In addition, assume that because the items are chosen at random, the outcomes of the choices are mutually independent. Finally, assume that the manufacturer's claim is correct. a. What is the probability that none of the ten is defective?

Answer 1

The probability that none of the ten items selected at random from a large batch are defective is approximately 73.74%.

Step-by-step explanation:

The student has asked about the probability of not having any defective items among ten chosen at random from a large batch. Since the probability of selecting a defective item is given as 0.03, the probability of selecting a non-defective item is 1 - 0.03 = 0.97. As the choices are independent, the probability of all ten items being non-defective is calculated by raising the probability of selecting one non-defective item to the power of ten.

The calculation would be as follows:
P(all ten non-defective) = 0.9710
Using a calculator, this equals approximately 0.7374, or 73.74%.