Question

Do you use probability in your profession or 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 chosen profession 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. Post your initial response early, and check back often to continue the discussion. Be sure to respond to your peers’ and instructor’s posts, as well.

Answer 1

Answer:

(i)Let B=The event a student gets a job

Let A=The event that a student that a student takes statistics subject as a major.

Two events are mutually exclusive.A clear example is the set of a single coin toss,which can result in either heads or tails,but not both.

In this example,the events of A and B are not mutually exclusive.

Hence,

P(A or B)=P(A $\cup$ B)=P(A)+P(B)-P(A $\cap$ B)

(ii) Again,taking the same example:

Let B=The event a student gets job.

Let A=The event that a student takes statistics subject as a major.

Hence,

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

An independent event is a likelihood that one event occurs in no way affects the likelihood  of the other event occuring. An case  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 $\cup$ B)=P(A)*P(B)

In this case ,the events A and B are not independent.

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

P(B|A)=P(A $\cap$ B)/P(A).

Where,

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