A certain item is sold in a box at a price of $ 20.00 each box. It is characteristic of production that 20% of these articles are defective. One buyer made the following proposal: in each box, he chooses 25 articles, at random, and paid per box:
$ 25.00, if no item, of the selected, is defective;
$ 17.00 if one or two items are defective;
$ 10.00 if three or more are defective.
What is best for the seller: keep its price of $ 20.00 per box or accept the buyer proposal?
Keep it 20 dollars. The probability that there are no defects among 25 is $.8^{25}$ < .0038.