What is the probability that you find zero defective units?

Question

The company that you work for is ordering a product from a different country. Your job as a quality control specialists is to test for defective products. In a shipment of 40 you will pull 3 units out and test them. If you find one defective unit, your company will send the entire shipment back. Suppose that 5 out of the 40 are actually defective.

Answer 1

Suchi,

As is usual in problems of this nature, you don't calculate based on the probabilities of defective units, but rather of the non-defective ones. Why? Because the probabilities of defective units don't "add up" properly (the way you think they might) when you take multiple samples. That's because you stop sampling immediately if you find a defective unit! Think of it this way: you only complete the test and pass the lot IF you have exactly three OK units in a row. THOSE probabilities DO add up properly (or, better to say, multiply up properly).

So if the individual probability of a defect is 1/8, then p(three OK in a row) = (7/8)^3.

By the way, this problem says a lot about why international market savvy of US kids is so low -- no manufacturer in their right mind would think about using a product with this high defect rate.