Question

3a. Do you use probability in your real life? You most likely do. For example, the chance of rain tomorrow is 27%. We hear similar probabilities in the media all the time. Similar probabilities could be found in other professions. Complete one of the following:

(i) Find an example of probability involving “A or B” that is used in your or real life. Explain the example. Are the events A and B in your example mutually exclusive? Which Addition Rule formula for P(A or B) applies? Be sure to cite the source of the information clearly.

(ii) Using a search engine, find an example of probability involving “A and B” that is used in your chosen profession or real life. Explain the example. Are the events A and B in your example independent? Which Multiplication Rule formula for P(A and B) applies? Be sure to cite the source of the information clearly.

(iii) Find an example involving conditional probability that is used in your chosen profession or real life. Explain the example. Be sure to cite the source of the information clearly.

Be sure to support your statements with logic and argument, citing any sources referenced.

(3b) Is there an industry that most of you deal with that already uses a bunch of probability and statistics to determine what you're going to pay them?

(3c) Did you know that there is a branch of mathematics solely dedicated to this practice? Can you find the name and tell us about them?

No plagiarism Please***

Answer 1

3. (a)

(i) Let A be the event that a student takes statistics subject as a major.

Let B be the event a student gets a job.

Two events (or propositions) are mutually exclusive or disjoint if they cannot both occur (be true). A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.

In this case, the event A and B are not mutually exclusive.

Therefore, P(A or B) = P(A U B) = P(A) + P(B) − P(A ∩ B)

(ii) Again, taking the same example:

Let A be the event that a student takes statistics subject as a major.

Let B be the event a student gets a job.

Therefore, the event "A and B" will imply that a student takes statistics as a major gets a job.

An independent event is a probability that one event occurs in no way affects the probability of the other event occurring. An example of two independent events is as follows; say you rolled a die and flipped a coin.

if A and B are independent then P(A and B) = P(A ∩ B) = P(A)*P(B)

In this example, the event A and B are not independent.

(iii) Using the same example of event A and B, the conditional probability can be defined as

P(B/A) = Probability of a student getting a job given that he has taken statistics as a major.

(3b) Market research is one of such industry.

Market research, which includes social and opinion research, is the systematic gathering and interpretation of information about individuals or organizations using statistical and analytical methods and techniques of the applied social sciences to gain insight or support decision making.

(3c) Yes. I was aware of the subject statistics. I have completed MSc in stats.

Statistics is a branch of mathematics dealing with the collection, organization, analysis, interpretation and presentation of data. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied.