What is wrong with the following statements? Please explain.

a.P (A or B) = 1.0 if P(A) = 0.6 and P(B) = 0.2

b.P (A and B) = - 0.38

c.P(A) = 1.35

d.P (A and B) = 0.8 if P(A) = 0.5 and P(B) = 0.2

2.Given that P(A) = 0.5, P(B) = 0.35 and P(A B) = 0.30, calculate the following:

a.P(A U B) =

b.P(the complement of B) =

c.P(the complement of the event "A or B") =

d.P(A|B) =

e.P(B|A) =

f.Are Events A and B independent? How do you know?

3.The following table is a summary of one of the key questions in the employee satisfaction survey for ABC Limited. If an employee is randomly selected, answer the questions below:

Do you smoke?

Do you smoke?

Gender Yes No

Male 60 130

Female 10 100

a.What is the probability that the selected employee is a male?

b.What is the probability that the employee is a smoker?

c.What is the probability that the selected employee is a smoker and is a female?

d.Given the fact that the selected employee is female, what is the probability that she is not a smoker?

e.What is the probability that the employee is non-smoker if it is a male?

f.What is the probability that the employee is either a smoker or female?

g.Are the events "being a smoker" and "gender" independent? How do you know?

4.A school has 250 seniors of whom 150 will be going to college next year. Fifty will be going directly to work. The remainder are taking a gap year. Fifty of the seniors going to college play sports. Thirty of the seniors going directly to work play sports. Five of the seniors taking a gap year play sports.

a.What is the probability that a senior is taking a gap year?

b.A student is selected at random. What is the probability that the selected student is going to work directly?

c.What is the probability that the selected students plays sport?

d.Are playing sports and going to college independent events? Justify your answer.

5. The following is a probability function used to depict the projected net income (in millions) in the coming year for ABC Limited:

Net Income (X) Probability (f(X))

-1.0 0. 24

0 0.18

1 0.48

2.5 b

a.Find the value of b.

b.What does "b" mean in this context?

c.What is the probability that the company is not profitable (net income less than 0) in the coming year?

d.What is the probability that the company makes more than $2 million in the coming year?

e.What is the expected net income for ABC Limited, i.e., what is the expected value of this probability distribution?

f.What is the standard deviation of expected net income?

6. Brooks Insurance Inc. wishes to offer life insurance to men age 60 via the Internet. Mortality tables indicate the likelihood of a 60-year-old man surviving another year is 0.98. If the policy is offered to five men age 60:

a. What is the probability all five men survive the year?

b. What is the probability that no one survives?

7. The probability that a person catches a cold during the cold and flu season is 0.4. Assume that 10 people are chosen at random. You are asked to calculate the probability of people getting flue.

a.What probability distribution is suitable for this question?

b.What is the probability that exactly four of them will catch a cold?

c.What is the probability of two or less people catching cold?

d.What is the probability of at least two people catching cold?

8. On average, you receive 3 junk e-mail every 6 hours. Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution.

a.What is the expected number of junk e-mails in one day?

b.What is the probability of receiving exactly two junk e-mails in a six hours interval?

c.What is the probability of receiving less than two junk e-mails arrive in a six hour interval?

d.What is the probability of receiving two or more junk email in a six hours interval?