MAT 2051 Unit 3 DQ1 Networking and Probability

MAT 2051 Unit 3 DQ1 Networking and Probability

MAT 2051 Unit 3 DQ1 Networking and Probability

Question

MAT 2051 Discrete Mathematics

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:

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?

What is the
sample space in this problem?

Is this a
ratio of combinations or permutations problem? Explain why and show an example.
Hint: Read section 6.5 and see Example 6.5.4 in your textbook.

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?

Review the
Discussion Participation Scoring Guide prior to posting.

Response
Guidelines

Read your
peers’ posts and respond to two. Do you agree with your peer’s assessment?
Explain.

DQ2 Practice
Problem Set Review

This
discussion allows you to work with your peers to complete and understand the
assigned problem set for this unit. Remember, two initial posts and two
response posts are required. Further posts are optional and recommended:

For the
first post, select a problem from this unit’s problem set, write it out fully,
solve it fully, and post it.

The second
post can be a problem you cannot solve or another fully solved problem from the
problem set. If there is a problem in the problem set that you are confused
about, write it out fully and show any work that you have started. Note that you
are stuck and ask for help. If you are able to solve every problem in the set
without difficulty, post at least one other fully solved problem from the set
as your second post.

The third
and fourth posts are responses. Response guidelines are provided below and in
every discussion.

Take
advantage of this discussion area to work together as a class on the problem
set. Post as many problems as you can and review as many of your peers’ posts
as you can. Ask questions. Offer answers. If you are stuck on a problem, post
your question. Working as a team will help each person gain a better
understanding of the problem set and the concepts covered in this unit.
Although the problem sets are not graded they will help you prepare for the
quizzes in this course.

Response
Guidelines

The third
and fourth posts, the response posts, are your chance to help your peers.
Explore the posts made by your peers and find people who are stuck. Help at
least two peers through the problems they are stuck on. If you are unable to locate
a peer who is stuck, you may instead choose a peer post, write out your
solution to the same problem, and compare solutions and methods. The goal of
this area is for the entire class to work together as a group on the entire
problem set. You are also expected to complete and understand the problem set
on your own in preparation for the quizzes and final exam.

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