Exercises.

1. Let N =14, S =6, and n =5. Using the hypergeometric probability distribution formula, find

a) ; b) ; c)

2. Let N =16, S =10, and n =5. Using the hypergeometric probability distribution formula, find

a) ; b) ; c)

3. There are 25 goods, 5 of which are defective. We randomly select 4 goods. What is the probability that three of those four goods are nondefective and one is defective?

4. A committee of two members is to be formed from the list of 8 candidates. Of the 8 candidates, 5 are management and 3 are economics department students. Find the probability that

a) both candidates are managers

b) neither of the candidates are managers

c) at most one of the candidates is a manager.

5. A company buys keyboards from another company. The keyboards are received in shipments of 100 boxes, each box containing 20 keyboards. The quality control department first randomly selects one box from each shipment, and then randomly selects five keyboards from that box. The shipment is accepted if not more than one of the five keyboards is defective. The quality control inspector selects a box from a recently received shipment of keyboards. Unknown to the inspector, this box contains six defective keyboards.

a) What is the probability that this shipment will be accepted?

b) What is the probability that this shipment will not be accepted?

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