Part 1

Networking and Probability

Probability and statistics allow us to make decisions when dealing with uncertain variables. For example, assume you are the network administrator of a large firm and have ordered 100 RAID (redundant array of independent disks) devices. You would like to make sure all of the RAIDs work before sending them to different departments. But you do not have time to check all of the devices. If you check some of them and show they work, how confident could you be that all 100 devices work?

Of course, testing all of the RAIDs would be the best way to be confident, but assume you do not have the time. If you only have time to check 5 of the 100, and none of the 5 are defective, how confident would you be that none of the other microprocessors are defective (that is, all 100 devices are fully functional)?

Answer the following questions, which will help you understand the problem. Explain each question and your answer:

1.How can you use discrete probability to calculate the probability of testing 5 devices such that all 5 end up being nondefective RAIDs, given there are 20 defective RAIDs total of the original 100 RAID devices?

2.What is the sample space in this problem?

3.Is this a ratio of combinations or permutations problem? Explain why and show an example.

4.Assume there are exactly 5 defective RAIDs out of the 100 RAID devices. What is the probability of testing 20 RAIDs at random and finding all of them nondefective?

Part 2

Section 6.1, pages 274275, exercises 9 and 33.

Use the Multiplication Principle to solve

9.A restaurant chain advertised a special in which a customer could choose one of five appetizers, one of 14 main dishes, and one of three desserts. The ad said that there were 210 possible dinners. Was the ad correct? Explain.

33. In Exercises 2830, suppose there are 10 roads from Oz to Mid Earth and five roads from Mid Earth to Fantasy Island.

How many eight-bit strings have either the second or the fourth bit 1 (or both)?

Section 6.2, pages 288291, exercises 14 and 41.

In Exercises 1018, determine how many strings can be formed by ordering the letters ABCDE subject to the conditions given.

14. Aappears beforeD. Examples:BCAED, BCADE

41. How many eight-bit strings contain three 0s in a row and five 1s?