1.
Nineteen percent of all liquid crystal displays (LCDs) are manufactured by Samsung. What is the probability that in a collection of three independent LCD purchases, at least one is a Samsung? (Round your answer to 3 decimal places.)
2. A study of 200 advertising firms revealed their income after taxes:
Income after Taxes Number of Firms
Under $1 million 103
$1 million to $20 million 52
$20 million or more 45
________________________________________
(a) What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.)
(b-1) What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? (Round your answer to 2 decimal places.)
(b-2) What rule of probability could be applied?
3.
An Internet company located in Southern California has season tickets to the Los Angeles Lakers basketball games. The company president always invites one of the 7 vice presidents to attend games with him, and claims he selects the person to attend at random. One of the 7 vice presidents has not been invited to attend any of the last 3 Lakers home games.
What is the likelihood this could be due to chance? (Round your answer to 3 decimal places.)
4.
Refer to the following table.
|
First Event
|
|
|
|
|
|
|
Second Event
|
A1
|
A2
|
A3
|
Total
|
|
B1
|
4
|
2
|
6
|
12
|
|
B2
|
4
|
4
|
5
|
13
|
|
|
|
|
|
|
|
Total
|
8
|
6
|
11
|
25
|
|
|
|
|
|
|
| |
(a) Determine P(A1). (Round your answer to 2 decimal places.)
(b) Determine P(B2|A2). (Round your answer to 2 decimal places.)
(c) Determine P(B2 and A3). (Round your answer to 2 decimal places.)
5.
All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .72, the probability the second truck is available is .51, and the probability that both trucks are available is .42:
What is the probability neither truck is available? (Round your answer to 2 decimal places.)
6.
The probability a HP network server is down is .065. If you have four independent servers, what is the probability that at least one of them is operational? (Round your answer to 6 decimal places.)
7.
There are 26 families living in the Willbrook Farms Development. Of these families 13 prepared their own federal income taxes for last year, 10 had their taxes prepared by a local professional, and the remaining 3 by H&R Block.
(a) What is the probability of selecting a family that prepared their own taxes? (Round your answers to 3 decimal places.)
(b) What is the probability of selecting two families both of which prepared their own taxes? (Round your answers to 3 decimal places.)
(c) What is the probability of selecting three families, all of which prepared their own taxes? (Round your answers to 3 decimal places.)
(d) What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block? (Round your answers to 3 decimal places.)
8.
An overnight express company must include six cities on its route. How many different routes are possible, assuming that it matters in which order the cities are included in the routing?
9.
The events and are mutually exclusive. Suppose and
(a) What is the probability of either or occuring? (Round your answer to 2 decimal places.)
(b) What is the probability that neither nor will happen? (Round your answer to 2 decimal places.)
10.
In each of the following cases, indicate whether classical, empirical, or subjective probability is used.
(a) A baseball player gets a hit in 38 out of 54 times at bat. The probability is .70 that he gets a hit in his next at bat.
(b) A seven-member committee of students is formed to study environmental issues. What is the likelihood that any one of the seven is chosen as the spokesperson?
(c) You purchase one of 8 million tickets sold for Lotto Canada. What is the likelihood you win the $3 million jackpot?
(d) The probability of an earthquake in northern California in the next 9 years is .65.
Four sports teams remain in a single-elimination playoff competition. If one team is favored in its semi-final match by odds of 1.30 to 1.70 and another squad is favored in its contest by odds of 2.20 to 1.80. What is the probability that:
11.
(a) Both favored teams win their games? (Round your answer to 4 decimal places.)
12.
(b) Neither favored team wins its game? (Round your answer to 4 decimal places.)
13.
(c) At least one of the favored teams wins its game? (Round your answer to 4 decimal places.)
14.
The credit department of Lion's Department Store in Anaheim, California, reported that 24 percent of their sales are cash or check, 22 percent are paid with a credit card and 54 percent with a debit card. Twenty percent of the cash or check purchases, 90 percent of the credit card purchases, and 60 percent of the debit card purchases are for more than $50.
Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability she paid cash or check? (Round your answer to 3 decimal places.)
15.
A survey of 35 students at the Wall College of Business showed the following majors:
Accounting 11
Finance 6
Economics 4
Management 6
Marketing 8
________________________________________
Suppose you select a student and observe his or her major.
(a) What is the probability he or she is a management major? (Round your answer to 3 decimal places.)
(b) Which concept of probability did you use to make this estimate?
16.
A recent survey reported in BusinessWeek dealt with the salaries of CEOs at large corporations and whether company shareholders made money or lost money.
CEO Paid
More Than
$1 Million CEO Paid
Less Than
$1 Million Total
Shareholders made money 5 10 15
Shareholders lost money 8 7 15
Total 13 17 30
________________________________________
If a company is randomly selected from the list of 30 studied, calculate the probabilities for the following :
(a) The CEO made more than $1 million. (Round your answers to 3 decimal places.)
(b) The CEO made more than $1 million or the shareholders lost money. (Round your answers to 3 decimal places.)
(c) The CEO made more than $1 million given the shareholders lost money. (Round your answers to 3 decimal places.)
(d) Select 2 CEOs and find that they both made more than $1 million. (Round your answers to 3 decimal places.)
17.
A student is taking two courses, history and math. The probability the student will pass the history course is .50, and the probability of passing the math course is .71. The probability of passing both is .48.
What is the probability of passing at least one? (Round your answer to 2 decimal places.)
18.
The events X and Y are mutually exclusive. Suppose P(X) = .07 and P(Y) = .05.
(1) What is the probability of either X or Y occurring? (Round your answer to 2 decimal places.)
(2) What is the probability that neither X nor Y will happen? (Round your answer to 2 decimal places.)
[The following information applies to the questions displayed below.]
Joe Mauer of the Minnesota Twins had the highest batting average in the 2009 Major League Baseball season. His average was .268. So assume the probability of getting a hit is .268 for each time he batted. In a particular game, assume he batted two times.
19.
(a) This is an example of what type of probability?
20.
(b) What is the probability of getting two hits in a particular game? (Round your answer to 3 decimal places.)
21.
(c) What is the probability of not getting any hits in a game? (Round your answer to 3 decimal places.)
22.
(d) What is the probability of getting at least one hit? (Round your answer to 3 decimal places.)
[The following information applies to the questions displayed below.]
A sample of 45 oil industry executives was selected to test a questionnaire. One question about environmental issues required a yes or no answer.
23.
1. Which of the following are possible events. (Select all that apply.)
43 people respond "Yes."
42 people respond "Yes."
28 people respond "No."
50 people respond "No."
The questionnaire fails to reach one executive.
24.
Eight of the 45 executives responded "Yes." Based on these sample responses, what is the probability that an oil industry executive will respond "Yes"? (Round your answer to 2 decimal places.)
25.
What concept of probability does this illustrate?
26.
Are each of the possible outcomes equally likely and mutually exclusive?
27.
Assume there are 24 homes in the Quail Creek area and 7 of them have a security system. Five homes are selected at random:
(a) What is the probability all five of the selected homes have a security system? (Round your answer to 4 decimal places.)
(b) What is the probability none of the five selected homes have a security system? (Round your answer to 4 decimal places.)
(c) What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.)
(d) Are the events dependent or independent?
28.
You take a trip by air that involves three independent flights. If there is an 82 percent chance each specific leg of the trip is done on time, what is the probability all three flights arrive on time? (Round your answer to 3 decimal places.)
29.
Solve the following:
(a)
(b)
9P5 =
(c)
9C6 =