Statistics 2

1.

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

results.

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.

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more