Question 1

A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non-defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items.
a.An item from the production line is selected. What is the probability that the selected item is non-defective?
b.Given that the selected item is non-defective, what is the probability that the machine is set up correctly?

Accepted Answer

The answer of A machine is used in a production...

Question 2

A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?

Accepted Answer

The answer of A company plans to interview 10 recent...

Question 3

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?

Accepted Answer

A) 1/52 
B) 2/52 
C) 3/52 
D) 4/52

Question 4

The multiplication law is potentially helpful when we are interested in computing the probability of

Accepted Answer

A) mutually exclusive events 
B) the intersection of two events 
C) the union of two events 
D) conditional events

Question 5

Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is

Accepted Answer

A) one 
B) any positive value 
C) zero 
D) any value between 0 to 1

Question 6

Records of a company show that 15% of the employees have only a high school diploma; 75% have bachelor degrees; and 10% have graduate degrees. Of those with only a high school diploma, 12% hold management positions; whereas, of those having bachelor degrees, 58% hold management positions. Finally, 82% of the employees who have graduate degrees hold management positions.
a.What percentage of employees holds management positions?
b.Given that a person holds a management position, what is the probability that she/he has a graduate degree?

Accepted Answer

The answer of Records of a company show that 15%...

Question 7

A graphical device used for enumerating sample points in a multiple-step experiment is a

Accepted Answer

A) bar chart 
B) pie chart 
C) histogram 
D) None of these alternatives is correct.

Question 8

A committee of 4 is to be selected from a group of 12 people. How many possible committees can be selected?

Accepted Answer

The answer of A committee of 4 is to be...

Question 9

The symbol $\cup$ shows the

Accepted Answer

A) union of events 
B) intersection of two events 
C) sum of the probabilities of events 
D) sample space

Question 10

A method of assigning probabilities which assumes that the experimental outcomes are equally likely is referred to as the

Accepted Answer

A) objective method 
B) classical method 
C) subjective method 
D) experimental method

Question 11

If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then, P(A $\cup$ B) =

Accepted Answer

A) 0.07 
B) 0.62 
C) 0.55 
D) 0.48

Question 12

From a group of seven finalists to a contest, three individuals are to be selected for the first and second and third places. Determine the number of possible selections.

Accepted Answer

The answer of From a group of seven finalists to...

Question 13

If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A $\cap$ B) =

Accepted Answer

A) 0.76 
B) 1.00 
C) 0.24 
D) 0.20

Question 14

The intersection of two mutually exclusive events

Accepted Answer

A) can be any value between 0 to 1 
B) must always be equal to 1 
C) must always be equal to 0 
D) can be any positive value

Question 15

Assume you have applied for two jobs A and B. The probability that you get an offer for job A is 0.23. The probability of being offered job B is 0.19. The probability of getting at least one of the jobs is 0.38.
a.What is the probability that you will be offered both jobs?
b.Are events A and B mutually exclusive? Why or why not? Explain.

Accepted Answer

The answer of Assume you have applied for two jobs...

Question 16

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is

Accepted Answer

A) 9 
B) 14 
C) 24 
D) 36

Question 17

In a recent survey of computer ownership, 73.4% of the respondents indicated they own PC computers, while 21.8% indicated they own both PC and Mac computers, and 80.1% said they own at least one of the two computers.
a.What is the probability that a respondent owns a Mac computer?
b.Given that a respondent owns a PC, what is the probability that the respondent also owns a Mac?
c.Are events "P" and "M" mutually exclusive? Why or why not? Explain using probabilities.
d.Are the two events "P" and "M" independent? Explain, using probabilities.

Accepted Answer

The answer of In a recent survey of computer ownership,...

Question 18

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the

Accepted Answer

A) relative frequency method 
B) subjective method 
C) classical method 
D) posterior method

Question 19

Any process that generates well-defined outcomes is

Accepted Answer

A) an event 
B) an experiment 
C) a sample point 
D) a sample space

Question 20

If P(A) = 0.50, P(B) = 0.60, and P(A $\cap$ B) = 0.30, then events A and B are

Accepted Answer

A) mutually exclusive events 
B) not independent events 
C) independent events 
D) not enough information is given to answer this question

Exam 4: Introduction to Probability