1)Probabilities that cannot be estimated from long-run relative frequencies of events are

1. 1. objective probabilities         c. complementary probabilities
   2. subjective probabilities        d. joint probabilities

 

 

 

 

2. The probability of an event and the probability of its complement always sum to:
   1. 1      c. any value between 0 and 1
   2. 0      d. any positive value

 

 

 

 

3. If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to
   1. 0.0   c. 1.0
   2. 0.5   d. any value between 0.5 and 1.0

 

 

 

 

4. Probabilities that can be estimated from long-run relative frequencies of events are
   1. objective probabilities         c. complementary probabilities
   2. subjective probabilities        d. joint probabilities

 

 

 

 

5. Let A and B be the events of the FDA approving and rejecting a new drug to treat hypertension, respectively. The events A and B are:
   1. independent             c. unilateral
   2. conditional d. mutually exclusive

 

 

 

 

6. A function that associates a numerical value with each possible outcome of an uncertain event is called a
   1. conditional variable             c. population variable
   2. random variable      d. sample variable

 

 

 

 

7. The formal way to revise probabilities based on new information is to use:
   1. complementary probabilities           c. unilateral probabilities
   2. conditional probabilities      d. common sense probabilities

 

 

 

 

8.  is the:

a. addition rule		c. rule of complements
b. commutative rule		d. rule of opposites

9. The law of large numbers is relevant to the estimation of
   1. objective probabilities         c. both of these options
   2. subjective probabilities        d. neither of these options

 

 

 

 

 

10. A discrete probability distribution:
    1. lists all of the possible values of the random variable and their corresponding probabilities
    2. is a tool that can be used to incorporate uncertainty into models
    3. can be estimated from long-run proportions
    4. is the distribution of a single random variable

 

 

 

 

11. Which of the following statements are true?
    1. Probabilities must be nonnegative
    2. Probabilities must be less than or equal to 1
    3. The sum of all probabilities for a random variable must be equal to 1
    4. All of these options are true.

 

 

 

 

12. If P(A) = P(A|B), then events A and B are said to be
    1. mutually exclusive c. exhaustive
    2. independent             d. complementary

 

 

 

 

13. If A and B are mutually exclusive events with P(A) = 0.70, then P(B):
    1. can be any value between 0 and 1
    2. can be any value between 0 and 0.70
    3. cannot be larger than 0.30
    4. Cannot be determined with the information given

 

 

 

 

14. If two events are collectively exhaustive, what is the probability that one or the other occurs? a. 0.25
    2. 0.50
    3. 1.00
    4. Cannot be determined from the information given.

 

 

 

 

15. If two events are collectively exhaustive, what is the probability that both occur at the same time? a. 0.00
    2. 0.50
    3. 1.00
    4. Cannot be determined from the information given.

 

 

 

 

 

 

 

16. If two events are mutually exclusive, what is the probability that one or the other occurs? a. 0.25
    2. 0.50
    3. 1.00
    4. Cannot be determined from the information given.

 

 

 

 

17. If two events are mutually exclusive, what is the probability that both occur at the same time? a. 0.00
    2. 0.50
    3. 1.00
    4. Cannot be determined from the information given.

 

 

 

 

18. If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?
    1. 0.00
    2. 0.50
    3. 1.00
    4. Cannot be determined from the information given.

 

 

 

 

19. There are two types of random variables, they are
    1. discrete and continuous       c. complementary and cumulative
    2. exhaustive and mutually exclusive d. real and unreal

 

 

 

 

20. If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is:
    1. 0.25
    2. 0.40
    3. 0.90
    4. Cannot be determined from the information given

 

 

 

 

21. If two events are independent, what is the probability that they both occur? a. 0
    2. 0.50
    3. 1.00
    4. Cannot be determined from the information given

 

 

 

 

22. If A and B are any two events with P(A) = .8 and P(B|) = .7, then P(and B) is
    1. .56   c. .24
    2. .14   d. None of the above

 

 

 

 

23. Which of the following best describes the concept of marginal probability?
    1. It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs.
    2. It is a measure of the likelihood that a particular event will occur, given that another event has already occurred.
    3. It is a measure of the likelihood of the simultaneous occurrence of two or more events. d. None of the above.

 

 

 

 

 

24. If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then the probability that either A or B or both occur is:
    1. 0.10             c. 0.70
    2. 0.12             d. None of the above

 

 

 

 

25. If A and B are any two events with P(A) = .8 and P(B|A) = .4, then the joint probability of A and B is
    1. .80   c. .32
    2. .40   d. 1.20

 

 

 

 

TRUE/FALSE

 

1. If A and B are independent events with P(A) = 0.40 and P(B) = 0.50, then P(A/B) is 0.50.

 

 

 

2. A random variable is a function that associates a numerical value with each possible outcome of a random phenomenon.

 

 

 

3. Two or more events are said to be exhaustive if one of them must occur.

 

 

 

4. You think you have a 90% chance of passing your statistics class. This is an example of subjective probability.

 

 

 

5. The number of cars produced by GM during a given quarter is a continuous random variable.

 

 

 

6. Two events A and B are said to be independent if P(A and B) = P(A) + P(B)

 

 

 

7. Probability is a number between 0 and 1, inclusive, which measures the likelihood that some event will occur.

 

 

 

8. If events A and B have nonzero probabilities, then they can be both independent and mutually exclusive.

 

 

 

9. The probability that event A will not occur is denoted as .

 

 

 

10. If P(A and B) = 1, then A and B must be collectively exhaustive.

 

 

 

11. Conditional probability is the probability that an event will occur, with no other events taken into consideration.

 

 

 

12. When we wish to determine the probability that at least one of several events will occur, we would use the addition rule.

 

 

 

13. The law of large numbers states that subjective probabilities can be estimated based on the long run relative frequencies of events

 

 

 

14. Two events are said to be independent when knowledge of one event is of no value when assessing the probability of the other.

 

 

 

15. Suppose A and B are mutually exclusive events where P(A) = 0.2 and P(B) = 0.5, then P(A or B) =

 

 

 

 

16. If A and B are two independent events with P(A) = 0.20 and P(B) = 0.60, then P(A and B) = 0.80

 

 

 

17. The relative frequency of an event is the number of times the event occurs out of the total number of times the random experiment is run.

 

 

 

18. Marginal probability is the probability that a given event will occur, given that another event has already occurred.

 

 

 

19. The temperature of the room in which you are writing this test is a continuous random variable.

 

 

 

20. Two events A and B are said to mutually be exclusive if P(A and B) = 0.

 

 

 

21. Two or more events are said to be exhaustive if at most one of them can occur.

 

 

 

22. When two events are independent, they are also mutually exclusive.

 

 

 

23. Two or more events are said to be mutually exclusive if at most one of them can occur.

 

 

 

24. Given that events A and B are independent and that P(A) = 0.8 and P(B/A) = 0.4, then P(A and B) =

 

 

 

 

25. The time students spend in a computer lab during one day is an example of a continuous random variable.

 

 

 

26. The multiplication rule for two events A and B is: P(A and B) = P(A|B)P(A).

 

 

 

27. The number of car insurance policy holders is an example of a discrete random variable.

 

 

 

28. Suppose A and B are mutually exclusive events where P(A) = 0.3 and P(B) = 0.4, then P(A and B) =

 

 

 

 

29. Suppose A and B are two events where P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2, then P(B/A) =

 

 

 

 

30. Suppose that after graduation you will either buy a new car (event A) or take a trip to Europe (event B). Events A and B are mutually exclusive.

 

 

 

31. If P(A and B) = 0, then A and B must be collectively exhaustive.

 

 

 

32. The number of people entering a shopping mall on a given day is an example of a discrete random variable.

 

 

 

33. Football teams toss a coin to see who will get their choice of kicking or receiving to begin a game. The probability that given team will win the toss three games in a row is 0.125.

 

 

 

SHORT ANSWER

 

 

 

1. Find the probability distribution of X.

 

 

 

 

 

 

2. What is the probability that this project will be completed in less than 4 months from now?

 

 

 

 

3. What is the probability that this project will not be completed on time?

 

 

 

 

 

4. (A) What is the expected completion time (in months) from now for this project?

 

(B) How much variability (in months) exists around the expected value found in (A)?

 

 

 

 

 

 

 

 

5. Find the marginal distribution of X. What does this distribution tell you?

 

 

 

 

 

6. Find the marginal distribution of Y. What does this distribution tell you?

 

 

 

 

7. (A) Calculate the conditional distribution of X given Y.

 

(B) What is the practical benefit of knowing the conditional distribution in (A)?

 

 

 

 

 

8. Calculate the conditional distribution of Y given X.

 

   

 

 

 

 

9. What is the probability that no one is waiting or being served in the regular checkout line?

 

 

 

 

10. What is the probability that no one is waiting or being served in the express checkout line?

 

 

 

 

11. What is the probability that no more than two customers are waiting in both lines combined?

 

 

 

 

 

12. On average, how many customers would you expect to see in each of these two lines at the grocery store?

 

 

 

 

 

 

 

 

 

 

13. Find the expected price and demand level for the upcoming quarter.

 

 

 

 

14. What is the probability that the price of this product will be above its mean in the upcoming quarter?

 

 

 

 

15. What is the probability that the demand of this product will be below its mean in the upcoming quarter?

 

 

 

 

16. What is the probability that the demand of this product exceed 2500 units in the upcoming quarter, given that its price will be less than $30?

 

 

 

 

17. What is the probability that the demand of this product will be less than 3500 units in the upcoming quarter, given that its price will be greater than $20?

 

 

 

 

 

 

 

 

18. Are           independent random variables? Explain why or why not.

 

19. Calculate the joint probabilities of

    and

    .

 

 

 

 

 

 

 

20. Determine the marginal probability distribution of .

 

 

 

 

21. What is probability of observing the sale of at least one brand 1 bat and at least one brand 2 bat on the same day at this sporting goods store?

 

 

 

 

22. What is the probability of observing the sale of at least one brand 1 bat on a given day at this sporting goods store?

 

 

 

 

23. What is the probability of observing the sale of no more than two brand 2 bats on a given day at this sporting goods store?

 

 

 

 

24. Given that no brand 2 bats are sold on a given day, what is the probability of observing the sale of at least one brand 1 bicycle at this sporting goods store?

 

25. Set up a 22 contingency table for this situation.

 

 

26. Give an example of a simple event.

 

 

 

 

27. Give an example of a joint event.

 

 

 

 

28. What is the probability that a respondent chosen at random is a male?

 

 

 

 

29. What is the probability that a respondent chosen at random enjoys shopping for clothing?

 

 

 

 

 

30. What is the probability that a respondent chosen at random is a male and enjoys shopping for clothing?

 

 

 

 

31. What is the probability that a respondent chosen at random is a female and enjoys shopping for clothing?

 

 

 

 

32. What is the probability that a respondent chosen at random is a male and does not enjoy shopping for clothing?

 

 

 

 

 

33. What is the probability that a respondent chosen at random is a female or enjoys shopping for clothing?

 

 

 

 

34. What is the probability that a respondent chosen at random is a male or does not enjoy shopping for clothing?

 

 

 

 

35. What is the probability that a respondent chosen at random is a male or a female?

 

 

 

36. What is the probability that a respondent chosen at random enjoys or does not enjoy shopping for clothing?

 

 

37. Does consumer behavior depend on the gender of consumer? Explain using probabilities.

 

 

 

 

38. Construct the joint probability table.

 

 

 

39. What is the probability a randomly selected patron prefers wine?

 

 

 

 

40. What is the probability a randomly selected patron is a female?

 

 

 

 

41. What is the probability a randomly selected patron is a female who prefers wine?

 

 

 

 

42. What is the probability a randomly selected patron is a female who prefers beer?

 

 

 

 

43. Suppose a randomly selected patron prefers wine. What is the probability the patron is a male?

 

 

 

 

44. Suppose a randomly selected patron prefers beer. What is the probability the patron is a male?

 

 

 

 

45. Suppose a randomly selected patron is a female. What is the probability the patron prefers beer?

 

 

 

 

46. Suppose a randomly selected patron is a female. What is the probability that the patron prefers wine?

 

 

 

 

47. Are gender of patrons and drinking preference independent? Explain.

 

 

 

 

 

48. Find the probability distribution of X; the number of oil wells that will be successful.

 

 

 

 

 

 

49. What is the probability that none of the oil wells will be successful?

 

 

 

 

50. If a new pipeline will be constructed in the event that all three wells are successful, what is the probability that the pipeline will be constructed?

 

 

 

 

51. How many of the wells can the company expect to be successful?

 

 

 

 

52. Suppose the first well to be completed is successful. What is the probability that one of the two remaining wells is successful?

 

 

 

 

53. If it costs $200,000 to drill each well and a successful well will produce $1,000,000 worth of oil over its lifetime, what is the expected net value of this three-well program?