Chapter 5 MCQ Practice #2

Of the coffee makers sold in an appliance store, 5.0% have either a faulty switch or a defective cord, 2.7% have a faulty switch, and 0.8% have both defects. What percent of the coffee makers will have a defective cord?

1. 3.1%

2. 3.55%

3. 5.0%

4. 5.8%

5. 97.3%

1. 3.1%

A group of volunteers for a clinical trial consists of 78 women and 71 men. 18 of the women and 22 of the men have high blood pressure.  If one of the volunteers is selected at random find the probability that the person has high blood pressure given that it is a woman.

1. 0.268

2. 0.121

3. 0.231

4. 0.523

5. 0.450

3. 0.231

All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm.  Fifteen percent of the bags that do not contain forbidden material also trigger the alarm.  If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material?

1. 0.300

2. 0.00097

3. 0.14550

4. 0.00640

5. 0.970

4. 0.00640

Applicants for a job first submit a written application. Based on the written applications, 27% of the applicants are invited for a first interview.  Of those that have a first interview, 56% are rejected after the interview. What is the probability that a randomly selected applicant receives a first interview and is rejected after the interview?

1. 0.1512

2. 0.56

3. 0.1188

4. 0.6788

5. 0.83

1. 0.1512

You want to use simulation to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin. You assign the digits 0, 1, 2, 3, 4 to heads and 5, 6, 7, 8, 9 to tails. Using the following random digits to execute as many simulations as possible, what is your estimate of the probability?

                        19226  95034 05756 07118

1. 6/10

2. 5/10

3. 1/10

4. 1/20

5. 2/5

1. 6/10

Some employers use lie detector tests to screen job applicants. Lie detector tests are not completely reliable. Suppose that a polygraph can detect 65% of lies, but incorrectly identifies 16% of true statements as lies. A company gives its job applicants a polygraph test, asking "Did you tell the truth on your job application?" All the applicants answer "Yes", but the test identifies some of those answers as lies, thereby causing the person to fail the test. Suppose 90% of  the job applicants tell the truth during the polygraph test.  What is the probability that a person who fails the test was actually telling the truth?

1. 0.451

2. 0.16

3. 0.689

4. 0.311

5. 0.9

3. 0.689

A company is conducting a sweepstakes, and ships two boxes of game pieces to a particular store. 7% of the contents of box A are winners, while 2% of the contents of box B are winners. Box A contains 32% of the total tickets. If the contents of both boxes are mixed in a drawer and a ticket is chosen at random, what is the probability it is a winner?

1. 0.07

2. 0.045

3. 0.022

4. 0.09

5. 0.036

5. 0.036

A system has two components that operate in parallel, as shown in the diagram below.

Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. Let F denote the event that component 1 fails during one period of operation and G denote the event that component 2 fails during one period of operation. Suppose P(F)=0.20 and P(G)=0.03.  The component failures are independent. The probability that the system function properly during one period of operation is

1. 0.994

2. 0.970

3. 0.940

4. 0.776

5. 0.5

1. 0.994

A standard deck of 52 cards is acquired. For those who do not know, a deck of cards contains 4 suits (hearts, diamonds, clubs, and spades).  Hearts and diamonds are red, clubs and spades are black. There are 13 denominations of cards (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace).

 

If you select two cards (without replacement), what is the probability that you select at least one Ace?

1. 118/221

2. 15/34

3. 33/221

4. 1 - (39/52)

5. Answer not provided

3. 33/221

A standard deck of 52 cards is acquired. For those who do not know, a deck of cards contains 4 suits (hearts, diamonds, clubs, and spades).  Hearts and diamonds are red, clubs and spades are black. There are 13 denominations of cards (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace).

If you select two cards (without replacement), what is the probability that you select a black card and a red card?

1. 25/51

2. 26/51

3. 13/51

4. 13/102

5. Answer not provided

2. 26/51

If A and B are independent events with P(A^c) = 0.7 and P(B) = 0.5, then P(A U B) is

1. 0.15

2. 0.80

3. 0.85

4. 0.65

5. Answer not provided

4. 0.65

If the occurrence of event A does not change the probability of event B, then events A and B are

1. dependent

2. disjoint

3. correlated

4. independent

5. a trial

4. independent

In place of a die, the ancient Greeks would roll an astragalus. Suppose that one astragalus has four possible outcomes, which we will name King, Steward, Peasant, and Thief.  If Peasant is four times as likely as King and Thief is four times as likely as Steward, and King are Steward are equally likely, which of the following is closes to the probability that one roll of this astragalus results in Peasant?

1. 0.1

2. 0.2

3. 0.03

4. 0.5

5. 0.4

5. 0.4

A car dealership sells sedans, vans and SUVs only.  The dealership has a downtown office and a suburban office.  The number of vehicles in the various categories sold by the dealership during a particular year are shown in the table.

	Sedans	Vans	SUVs
Downtown Office	977	244	610
Suburban Office	421	361	326

If the vehicle was sold at the suburban office, find the probability that the vehicle sold was a sedan.

1. 977/2939

2. 997/1398

3. 977/1831

4. (1831/2939)(1398/2939)

5. Answer not provided

5. Answer not provided

A car dealership sells sedans, vans and SUVs only.  The dealership has a downtown office and a suburban office.  The number of vehicles in the various categories sold by the dealership during a particular year are shown in the table.

	Sedans	Vans	SUVs
Downtown Office	977	244	610
Suburban Office	421	361	326

 

Suppose that a vehicle is chosen at random from the list of all the vehicles sold by the dealership during that year. Let A be the event that the vehicle is a sedan and let B be the event that the vehicle was bought from the downtown office.  Which of the following are true?

1. Events A and B are independent and mutually exclusive.

2. Events A and B are independent but not mutually exclusive.

3. Events A and B are not independent but they are mutually exclusive.

4. Events A and B are not independent and not mutually exclusive.

5. It is impossible to tell from the information provided if A and B are independent.

4. Events A and B are not independent and not mutually exclusive.

A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04 respectively.  If any one component fails, the device will fail.  If the components fail independently of one another, what is the probability that the device will not fail in one year?

1. 0.01

2. 0.92

3. 0.078

4. 0.080

5. greater than 0.99

2. 0.92