Question 1129678: 1) A hamburger shop sells hamburgers with cheese, relish, lettuce, tomato, onion, mustard, or
ketchup. How many different hamburgers can be concocted using any 5 of the extras? (3 marks)
2) A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 11 members and any member can be elected to each position? (3 marks)
3) Two marbles are drawn at random without replacement from a box containing two blue marbles and three red marbles. Hint: Use B1, B2, R1, R2, R3 for marble names.
a. List the sample space for this experiment. (4 marks) E.g. (B1, B2)
b. Determine the probability of observing each of the following events:
A: {2 blue marbles are drawn}. (3 marks)
B: {a red and blue marble are drawn}. (3 marks)
C: {2 red marbles are drawn}. (3 marks)
4) Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2,…,E7 denote the sample points. The following probability assignments apply: P(E1) = 0.05, P(E2) = 0.20, P(E3) = 0.20, P(E4) = 0.25, P(E5) = 0.15, P(E6)= 0.10, and P(E7) = 0.05. Let
A = {E1, E4, E6}
B = {E2, E4, E7}
C = {E2, E3, E5, E7}
a. Find P(A), P(B), and P(C). (6 marks)
b. Find A U B and P(A U B). (4 marks)
c. Find A ∩ B and P(A ∩ B). (4 marks)
d. Are events A and C mutually exclusive? (2 marks)
e. Find Bc and P(Bc). (4 marks)
5) A survey of magazine subscribers showed that 45.8% rented a car during the past 12 months
for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons.
a. What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons? (4 marks)
b. What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons? (4 marks)
6) For two independent events, A and B, P(A) = 0.4 and P(B) = 0.2.
a) (3 marks)
b) (3 marks)
c) (3 marks)
7) According to the Ameriprise Financial Money Across Generations study, 9 out of 10 parents
with adult children ages 20 to 35 have helped their adult children with some type of financial assistance ranging from college, a car, rent, utilities, credit-card debt, and/or down payments for houses (Money, January 2009). The following table with sample data consistent with the study shows the number of times parents have given their adult children financial assistance to buy a car and to pay rent.
Buy a Car Pay Rent
Yes No
Yes 56 52
No 14 78
a) Develop a joint probability table and use it to answer the remaining questions. (4 marks)
b) Using the marginal probabilities for buy a car and pay rent, are parents more likely to assist their adult children with buying a car or paying rent? What is your interpretation of the marginal probabilities? (5 marks)
c) If parents provided financial assistance to buy a car, what it the probability that the parents assisted with paying rent? (2 marks)
d) If parents did not provide financial assistance to buy a car, what is the probability the parents assisted with paying rent? (2 marks)
e) Is financial assistance to buy a car independent of financial assistance to pay rent? Use probabilities to justify your answer. (3 marks)
f) What is the probability that parents provided financial assistance for their adult children by either helping buy a car or pay rent? (3 marks)
Answer by Alan3354(69443)   (Show Source):
|
|
|
