Question

1. A bank has developed a set of criteria for evaluating distressed credit of company. Companies that passed the test will go bankrupt (non-survivor) with probability 0.4. There are 55% of the companies passed the test. The probability that a company did not pass the test will subsequently survive is 0.10

a. What is the probability that a random company will survive (not going to bankrupt)?     

b. A random survived company is selected, what is the probability that company passed the test?

c. What is the probability that a company is a non-survivor, given that it passed the test? Is the test effective?

2. A high school studied about the interest of students in 2 subjects Mathematics and English. The result showed that 35% of students like Math, 40% of students like English, and 10% like both Math and English.

a. What percentage of students like Math or English?

b. What percentage of students like neither Math nor English?

3. Consider two boxes, the first contains 2 white and 5 black balls, the second contains 5 white and 6 black balls. We flip a fair coin and then draw a ball from the first box or the second box depending on whether the outcome was head or tail.

a. What is the probability that a selected ball is a black ball?

b.Given that a white ball was selected, what is the conditional probability that the outcome of the toss was head?

4. In a sneaker company of 20 people, 5 are the graduated employee and the rest are internship. Randomly selected 3 person of them. Calculate the probability that at least one of them is a graduated employee.

5. A fair coin is tossed several times until exactly 3 heads are obtained . Calculate probability that coin is tossed exactly 5 times

6. Calculate the probability of getting 3 five times or more times when roll the dice 7 times

7. The following table gives the number of male and female in an area by education category

	Male	Female
Primary school	325	330
Secondary school	275	250
High school	200	205
Under graduated	150	140
Post graduated	55	40

1. Suppose a person is randomly selected. What is the probability that person is a male?
2. What is the probability that a person, who is a female, is under-graduated?
3. What is the probability that a person, who is not post graduated, is a female?
4. Let A is the event that a person is under-graduated; B is the event that a person is a female. What is the relation of A and B: mutually exclusive, independent or both?

8. Two stocks A and B are known to be related in that both are in the same industry. The probability that stock A will go up in price tomorrow is 0.20, and the probability that both stocks A and B will go up tomorrow is 0.12. Suppose that tomorrow you find that stock A did go up in price. What is the probability that stock B went up as well?

9. A Drug manufacturer believes there is a 0.95 chance that the Food and Drug Administration (FDA) will approve a new drug the company plans to distribute if the results of current testing show that the drug causes no side effects. The manufacturer further believes there is a 0.50 probability that the FDA will approve the drug if the test shows that the drug does cause side effects. A physician working for the drug manufacturer believes there is a 0.20 probability that tests will show that the drug causes side effects. What is the probability that the drug will be approved by the FDA?

The probability that a consumer entering a retail outlet for microcomputers and software packages will buy a computer of a certain type is 0.15. The probability that the consumer will buy a particular software package is 0.10. There is a 0.05 probability that the consumer will buy both the computer and the software package. What is the probability that the consumer will buy the computer or the software package or both

Answer 1