Can you help me with this?

1.What is wrong with the following statements? Please explain. (8 points)

a.P(A) = 1.2

b.P(complement of A) = 0.7 given that P(A) = 0.4

c.P(A or B) = 0.8 if P(A) = 0.3 and P(B) = 0.4

d.P(A and B)

2.Given that P(A) = 0.4, P(B) = 0.52 and P(A and B) = 0.25, calculate the following: (12 points)

a.P(A or 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? Please use probabilities to justify your answer.

3.The following table is a summary of one of the key questions in the employee satisfaction survey for XYZ Limited.If an employee (a male) is randomly selected, answer the questions below: (14 points)

Do you plan to be with Company one year from now?

Branch

Yes

No

Downtown

45

5

Uptown

87

9

4.

a.What is the probability that he is from the Uptown branch?

b.What is the probability that he plans to be with the company one year from now?

c.What is the probability that he is from the Downtown branch and plan to be with the company one year from now?

d.What is the probability that he is from the Uptown branch or does not plan to be with the company one year from now?

e.What is the probability that he is from the Downtown branch if he plans to be with the company one year from now?

f.What is the probability that he plans to be with the company one year from now given that he is from the Uptown branch?

g.Are the events "Downtown Branch" and "plans to be with the company one year from now" independent? Justify your answer using probabilities.

5.Historically, 40% of visitors to the online store of ABC Limited made a purchase.35% of the visitors who made a purchase came to the online store through a web search engine. Also, 10% of visitors who did not make a purchase came to the online store through a web search engine. If a visitor comes to the online store through a web search engine, what is the probability that he or she will make a purchase? (Suggestion: To think through the problem, use a probability tree and "whether a visitor makes a purchase" as the first step to depict what is given. Use the Bayes Theorem to calculate the probability in question. You do not need to include the tree in your submission.). (4 points)