a class of 50 students obtained the following grades in a

Statistics 2







A   5            B   25             C     15            D     5


        If one student is selected at random, what is the probability that


a.          The student obtained a B ?


b.         The student obtained either a A or a C ?


c.           The student did not obtain a D ?


d.         The student did not obtain either a B or a C ?

















2.     A realty company has 100 homes listed for sale. Some of these homes

have fireplaces, some have garages, and some have neither. A

breakdown is provided in the two way classification table below.




                                                       Fireplace                     No Fireplace

                                                              (F)                                   (F)



                Garage  (G)                          50                                    30


                No Garage (G)                     10                                    10



a.                 If one of these 100 homes is selected at random,


i.   What is the probability that the home selected does not have a

                 fireplace ?


           ii.  What is the probability that the home selected has a fireplace or

a garage ?


          iii.   What is the probability that the home selected has neither a

                  fireplace nor a garage ?


           iv.   What is the probability that the home selected has a garage but

                   not a fireplace ?


            v.    What is the probability that the home selected has a garage,

given that it has a fireplace?


b.                Are the events F = Fireplace and G = Garage independent? Show

your proof.



C. Are the events F and G mutually exclusive?  Why?
































3.          A person has applied for positions at company A, company B and

company C. The probability of obtaining an offer from company A is 0.4, from company B is 0.3 and from C is 0.6. Assume that the three job offers will be independent.


a.     What is the probability that the person will receive job offers 

from all three companies?


b.    What is the probability that the person will receive a job offer

from company B only.


c.      What is the probability that the person will receive a job offer

from at least one of the three companies?


d.    What is the probability that the person will receive exactly one

job offer from the three companies?


HINT:  Construct a tree diagram

















 4.    A city council consists of 7 males and 4 females. Two councilors are

        selected at random to represent the city at an Elton John concert.

        What is the probability that



a.     Both councilors are male?


b.    One councilor is a male and one a female?


c.      At least one councilor is a female?


        NOTE:  Express probabilities to 4 decimal places of accuracy.


        HINT:   Construct a tree diagram.





















5.    A machine used in a production process is set up correctly 97% of

the time. Given that the machine is set up correctly, only 5% of the

items it produces are defective, while 95% are not defective. On the

other hand, if the machine is set up incorrectly, 60% of the items it

produces are defective, while only 40% are not defective.


       What is the probability that a randomly selected item from the

production process will not be defective?


       NOTE:   Express probabilities to 4 decimal places of accuracy.


       HINT:   Construct a tree diagram.
























6.      In a survey of 100 business executives, 60 percent were male and

         40 percent were female. Seventy percent of the male executives used

          a PDA (personal digital assistant). Overall, 60% of the executives

          used a PDA. Construct a two-way classification table for the survey






























7.    You are given the probabilities listed below.


P(A) = 0.25


P(B) = 0.30


        P(C) = 0.55


        P( A and C ) = 0.05


        P( B and C ) = 0


P(B|A) = 0.48



a.          Are A and B independent events?  Why or why not?


b.         Find P(A and B ).


c.          Find P(A or B )


d.         Find P(A|B).


e.          Are B and C mutually exclusive events? Why or y not?


f.            Are B and C independent events? Provide a mathematical proof.











University Writings
Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

Calculate the price of your order

Total price:

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.


Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.


Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.


Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.


Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.