Question 1. A developer of a new subdivision wants to build homes that are all different. There are three different interior plans that can be combined with any of five different home exteriors. How many different homes can be built?
8
10
15
30
Question 2. Six basic colors are used in decorating a new condominium. They are applied to a unit in groups of four colors. One unit might have gold as the principal color, blue as a complementary color, red as the accent color, and touches of white. Another unit might have blue as the principal color, white as the complementary color, gold as the accent color, and touches of red. If repetitions are permitted, how many different units can be decorated?
7,825
25
125
1,296
Question 3. In the Happy Hilltop Health Home, 10% of the residents play shuffleboard, 20% of the residents play poker, and 50% of the residents garden. If 15% of the residents play poker and garden and 30% of the residents play both shuffleboard and poker, then find the probability that a resident plays poker, given that they garden.
30%
40%
20%
50%
Question 4. An article titled" Pain and Pain related side effects in an ICU and on a surgical unit: Nurses' Management" (American Journal of Critical Care, January 1994, Vol 3, No:1) gave the following table summarizing the study participants. (Note that ICU is an acronym for Intensive care unit)
Given this person is a female, what is the probability that she is from ICU?
10/22
10/17
10/48
12/22
Question 5. Consider the following sample space, S, and several events defined on it. S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}. F ∩ H is ___________.
{Meagan}
{Betty, Patty, Abel, Meagan}
empty, since F and H are complements
empty, since F and H are independent
empty, since F and H are mutually exclusive
Question 6. Consider the following sample space, S, and several events defined on it. S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}. F ∪ H is ___________.
{Meagan}
{Betty, Abel, Patty, Meagan}
empty, since F and H are complements
empty, since F and H are independent
empty, since F and H are mutually exclusive
Question 7. It is known that 20% of all students in some large university are overweight, 20% exercise regularly and 2% are overweight and exercise regularly. What is the probability that a randomly selected student is either overweight or exercises regularly or both?
0.40
0.38
0.20
0.42
0.10
Question 8. Max Sandlin is exploring the characteristics of stock market investors. He found that sixty percent of all investors have a net worth exceeding $1,000,000; 20% of all investors use an online brokerage; and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage. An investor is selected randomly, and E is the event "net worth exceeds $1,000,000" and O is the event "uses an online brokerage". P(O ∪ E) = _____________.
0.17
0.50
0.80
0.70
0.10
Question 9. Suppose that 3% of all TVs made by some Company in 2012 are defective. If 2 of these TVs are randomly selected what is the probability that both are defective?
0.0009
0.0025
0.0900
0.0475
0.19
Question 10. The probability of A È B where A is receiving a state grant and B is receiving a federal grant is the probability of receiving no more than one of the two grants.
True
False
Question 11. The probability that an event, Event A, occurs is 0.70. The probability of another event, Event B, occurs 0.67. The probability of both A and B occur is 0.50. The probability that either Event A or Event B occurs is __________.
0.87
0.53
1.37
None of these answers are correct.
Question 12. How many different combinations of a 4-member debating team can be formed from a group of 10 qualified students?
5040
210
14
4
Question 13. Two operations must be done to finish a job. If the first operation may be done in four different ways and the second operation in six different ways, how many different ways are there to do the job?
10
6
4
24
Question 14. There is a 30% chance that the economy will be good next year and a 70% chance that it will be bad. If the economy is good, there is a 60% chance of a bull market, a 30% chance of a normal market, and a 10% chance of a bear market. If the economy is bad, there is a 15% chance of a bull market, 30% chance of a normal market, and a 55% chance of a bear market.
Given the market is a normal market next year, what is the probability that the economy is good?
0.30
0.45
0.31
0.70
Question 15. There is a 30% chance that the economy will be good next year and a 70% chance that it will be bad. If the economy is good, there is a 60% chance of a bull market, a 30% chance of a normal market, and a 10% chance of a bear market. If the economy is bad, there is a 15% chance of a bull market, 30% chance of a normal market, and a 55% chance of a bear market.
Given the market is a bull market next year, what is the probability that the economy is good?
0.63
0.30
0.48
0.60
Question 16. There is a 30% chance that the economy will be good next year and a 70% chance that it will be bad. If the economy is good, there is a 60% chance of a bull market, a 30% chance of a normal market, and a 10% chance of a bear market. If the economy is bad, there is a 15% chance of a bull market, 30% chance of a normal market, and a 55% chance of a bear market.
What is the probability of having a good economy and a bull market?
0.90
0.18
0.30
0.45