Test 1-Problem Set 4

24. If two events are mutually exclusive, then their intersection a. will be equal to zero b. can have any value larger than zero c. must be larger than zero, but less than one d. will be one

A

7. If P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B) a. is 0.00 b. is 1.00 c. is 0.5 d. None of these alternatives is correct.

D

40. Assume you have applied to two different universities (let's refer to them as Universities A and B) for your graduate work. In the past, 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the applicants. Assume events are independent of each other. a. What is the probability that you will be accepted in both universities? b. What is the probability that you will be accepted to at least one graduate program? c. What is the probability that one and only one of the universities will accept you? d. What is the probability that neither university will accept you?

a. 0.0875 b. 0.5125 c. 0.425 d. 0.4875

44. Assume that in your hand you hold an ordinary six-sided die and a dime. You toss both the die and the dime on a table. a. What is the probability that a head appears on the dime and a six on the die? b. What is the probability that a tail appears on the dime and any number more than 3 on the die? c. What is the probability that a number larger than 2 appears on the die?

a. 1/12 b. 3/12 c. 8/12

37. From among 8 students how many committees consisting of 3 students can be selected?

56

20. If a coin is tossed three times, the likelihood of obtaining three heads in a row is a. zero b. 0.500 c. 0.875 d. 0.125

D

10. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A | B) = a. 0.05 b. 0.0325 c. 0.65 d. 0.8

A

17. The set of all possible outcomes of an experiment is a. an experiment b. an event c. the population d. the sample space

D

2. When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the a. relative frequency method b. subjective method c. probability method d. classical method

D

26. If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then, P(A ∪B) = a. 0.07 b. 0.62 c. 0.55 d. 0.48

D

46. Assume that each year the IRS randomly audits 10% of the tax returns. If a married couple has filed separate returns, a. What is the probability that both the husband and the wife will be audited? b. What is the probability that only one of them will be audited? c. What is the probability that neither one of them will be audited? d. What is the probability that at least one of them will be audited?

a. 0.01 b. 0.18 c. 0.81 d. 0.19

43. All the employees of ABC Company are assigned ID numbers. The ID number consists of the first letter of an employee's last name, followed by four numbers. a. How many possible different ID numbers are there? b. How many possible different ID numbers are there for employees whose last name starts with an A?

a. 260,000 b. 10,000

25. If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A ∪B) = a. 0.65 b. 0.55 c. 0.10 d. 0.75

B

32. From nine cards numbered 1 through 9, two cards are drawn. Consider the selection and classification of the cards as odd or even as an experiment. How many sample points are there for this experiment? a. 2 b. 3 c. 4 d. 9

C

11. An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome E4 is a. 0.500 b. 0.024 c. 0.100 d. 0.900

C

9. Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is a. one b. any positive value c. zero d. any value between 0 to 1

C

30. The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed 2 times and event A did not occur, then on the third trial event A a. must occur b. may occur c. could not occur d. has a 2/3 probability of occurring

B

38. How many committees, consisting of 3 female and 5 male students, can be selected from a group of 5 female and 8 male students?

560

49. In a recent survey in a Statistics class, it was determined that only 60% of the students attend class on Fridays. From past data it was noted that 98% of those who went to class on Fridays pass the course, while only 20% of those who did not go to class on Fridays passed the course. a. What percentage of students is expected to pass the course? b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays?

a. 66.8% b. 0.88

13. If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.5, then P(A ∩ B) = a. 0.00 b. 0.10 c. 0.90 d. 0.20

A

18. The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called a. permutation b. combination c. multiple step experiment d. None of these alternatives is correct.

A

23. If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) = a. 0.400 b. 0.169 c. 0.390 d. 0.650

A

27. Two events with nonzero probabilities a. can be both mutually exclusive and independent b. can not be both mutually exclusive and independent c. are always mutually exclusive d. are always independent

B

4. The multiplication law is potentially helpful when we are interested in computing the probability of a. mutually exclusive events b. the intersection of two events c. the union of two events d. conditional events

B

1. Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is a. 0.25 b. 0.50 c. 1.00 d. 0.75

B

15. Which of the following statements is always true? a. -1 ≤ P(Ei) ≤ 1 b. P(A) = 1 - P(Ac) c. P(A) + P(B) = 1 d. ∑P ≥ 1

B

16. If a six sided die is tossed two times, the probability of obtaining two "4s" in a row is a. 1/6 b. 1/36 c. 1/96 d. 1/216

B

22. Two events are mutually exclusive a. if their intersection is 1 b. if they have no sample points in common c. if their intersection is 0.5 d. None of these alternatives is correct.

B

12. One of the basic requirements of probability is a. for each experimental outcome Ei, we must have P(Ei) ≥ 1 b. P(A) = P(Ac) - 1 c. if there are k experimental outcomes, then ∑P(Ei)=1 d. ∑P(Ei) ≥ 1

C

41. A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?

120

21. Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.) a. 2 b. 4 c. 12 d. 16

D

3. Assume your favorite football team has 2 games left to finish the season. The outcome of each game can be win, lose or tie. The number of possible outcomes is a. 2 b. 4 c. 6 d. 9

D

33. A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is a. 30 b. 100 c. 729 d. 1,000

D

6. Of five letters (A, B, C, D, and E), two letters are to be selected at random (i.e. the order of selection doesn't matter). How many possible selections are there? a. 20 b. 7 c. 5 d. 10

D

14. If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪B) = 0.88, then P(B | A) = a. 0.02 b. 0.03 c. 0.04 d. 0.05

C

19. On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and "cold" weather is .15. Are snow and "cold" weather independent events? a. only if given that it snowed b. no c. yes d. only when they are also mutually exclusive

C

29. If P(A) = 0.48, P(A ∪B) = 0.82, and P(B) = 0.54, then P(A ∩ B) = a. 0.3936 b. 0.3400 c. 0.2000 d. 1.0200

C

8. If a penny is tossed four times and comes up heads all three times, the probability of heads on the fourth trial is a. zero b. 0.0625 c. 0.5000 d. larger than the probability of tails

C

36. Tammy is a general contractor and has submitted two bids for two projects (A and B). The probability of getting project A is 0.65. The probability of getting project B is 0.77. The probability of getting at least one of the projects is 0.90. a. What is the probability that she will get both projects? b. Are the events of getting the two projects mutually exclusive? Explain, using probabilities. c. Are the two events independent? Explain, using probabilities.

a. 0.52 b. No, the intersection is not zero. c. No, P(A | B) = 0.6753 ≠ P(A)

28. Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female. How many sample points exist in the above experiment? a. 64 b. 32 c. 16 d. 4

A

31. The addition law is potentially helpful when we are interested in computing the probability of a. independent events b. the intersection of two events c. the union of two events d. conditional events

C

34. From a group of six people, two individuals are to be selected at random. How many possible selections are there? a. 12 b. 36 c. 15 d. 8

C

35. Bayes' theorem is used to compute a. the prior probabilities b. the union of events c. intersection of events d. the posterior probabilities

D

5. Initial estimates of the probabilities of events are known as a. sets b. posterior probabilities c. conditional probabilities d. prior probabilities

D

45. Assume you have applied for two jobs A and B. The probability that you get an offer for job A is 0.23. The probability of being offered job B is 0.19. The probability of getting at least one of the jobs is 0.38. a. What is the probability that you will be offered both jobs? b. Are events A and B mutually exclusive? Why or why not? Explain.

a. 0.04 b. No, because P(A ∩ B) ≠ 0

48. An automobile dealer has kept records on the customers who visited his showroom. Forty percent of the people who visited his dealership were female. Furthermore, his records show that 35% of the females who visited his dealership purchased an automobile, while 20% of the males who visited his dealership purchased an automobile. a. What is the probability that a customer entering the showroom will buy an automobile? b. A car salesperson has just informed us that he sold a car to a customer. What is the probability that the customer was female?

a. 0.26 b. 0.538

47. Records of a company show that 15% of the employees have only a high school diploma (H), 75% have bachelor degrees (B), and 10% have graduate degrees (G). Of those with only a high school diploma, 12% hold management positions; whereas, of those having bachelor degrees, 58% hold management positions. Finally, 82% of the employees who have graduate degrees hold management positions. a. What percentage of employees holds management positions? b. Given that a person holds a management position, what is the probability that she/he has a graduate degree?

a. 0.538 b. 0.1533

39. A corporation has 15,000 employees. Sixty-two percent of the employees are male. Twenty-three percent of the employees earn more than $30,000 a year. Eighteen percent of the employees are male and earn more than $30,000 a year. a. If an employee is taken at random, what is the probability that the employee is male? b. If an employee is taken at random, what is the probability that the employee earns more than $30,000 a year? c. If an employee is taken at random, what is the probability that the employee is male and earns more than $30,000 a year? d. If an employee is taken at random, what is the probability that the employee is male or earns more than $30,000 a year? e. The employee is taken at random turns out to be male. Compute the probability that he earns more than $30,000 a year. f. Are being male and earning more than $30,000 a year independent?

a. 0.62 b. 0.23 c. 0.18 d. 0.67 e. 0.2903 f. No

42. As a company manager for Claimstat Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion, a raise, or both. The probability of getting a promotion and a raise is 0.25. a. If you get a promotion, what is the probability that you will also get a raise? b. What is the probability that you will get a raise? c. Are getting a raise and being promoted independent events? Explain using probabilities. d. Are these two events mutually exclusive? Explain using probabilities.

a. 0.625 b. 0.57 c. No, because P(R) ≠ P(R | P) d. No, because P(R ∩ P) ≠ 0