Deck 4: Introduction to Probability

Question 1

From a group of six people, two individuals are to be selected at random. How many possible selections are there?

A) 12
B) 36
C) 15
D) 8

Answer 1

C

Question 2

The intersection of two mutually exclusive events

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

Answer 2

C

Question 3

The sample space refers to

A) any particular experimental outcome
B) the sample size minus one
C) the set of all possible experimental outcomes
D) an event

Answer 3

C

Question 4

Which of the following statements is always true?

A) -1 ≤ PEi) ≤ 1
B) PA) = 1 - A^c)
C) PA) + PB) = 1
D) ∑P ≥ 1

Question 5

Each individual outcome of an experiment is called

A) the sample space
B) a sample point
C) an experiment
D) an individual

Question 6

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

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

Question 7

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called

A) permutation
B) combination
C) multiple step experiment
D) None of these alternatives is correct.

Question 8

An experiment consists of selecting a student body president and vice president. All undergraduate students freshmen through seniors) are eligible for these offices. How many sample points possible outcomes as to the classifications) exist?

A) 4
B) 16
C) 8
D) 32

Question 9

Two events are mutually exclusive

A) if their intersection is 1
B) if they have no sample points in common
C) if their intersection is 0.5
D) None of these alternatives is correct.

Question 10

Events that have no sample points in common are

A) independent events
B) posterior events
C) mutually exclusive events
D) complements

Question 11

A graphical method of representing the sample points of an experiment is

A) a frequency polygon
B) a histogram
C) an ogive
D) a tree diagram

Question 12

The range of probability is

A) any value larger than zero
B) any value between minus infinity to plus infinity
C) zero to one
D) any value between -1 to 1

Question 13

A sample point refers to the

A) numerical measure of the likelihood of the occurrence of an event
B) set of all possible experimental outcomes
C) individual outcome of an experiment
D) sample space

Question 14

The collection of all possible sample points in an experiment is

A) the sample space
B) a sample point
C) an experiment
D) the population

Question 15

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

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

Question 16

When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the

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

Question 17

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called

A) permutation
B) combination
C) multiple step experiment
D) None of these alternatives is correct.

Question 18

In statistical experiments, each time the experiment is repeated

A) the same outcome must occur
B) the same outcome can not occur again
C) a different outcome may occur
D) a different out come must occur

Question 19

A method of assigning probabilities based upon judgment is referred to as the

A) relative method
B) probability method
C) classical method
D) subjective method

Question 20

Any process that generates well-defined outcomes is

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

Question 21

The sum of the probabilities of two complementary events is

A) Zero
B) 0.5
C) 0.57
D) 1.0

Question 22

Initial estimates of the probabilities of events are known as

A) sets
B) posterior probabilities
C) conditional probabilities
D) prior probabilities

Question 23

If A and B are independent events with PA) = 0.65 and PA ∩ B) = 0.26, then, PB) =

A) 0.400
B) 0.169
C) 0.390
D) 0.650

Question 24

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?

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

Question 25

If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is

A) much larger than any other outcome
B) much smaller than any other outcome
C) 1/6
D) 1/216

Question 26

Three applications for admission to a local university are checked, and it is determined whether each applicant is male or female. The number of sample points in this experiment is

A) 2
B) 4
C) 6
D) 8

Question 27

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

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

Question 28

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

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

Question 29

Of five letters A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there?

A) 20
B) 7
C) 5!
D) 10

Question 30

Two events with nonzero probabilities

A) can be both mutually exclusive and independent
B) can not be both mutually exclusive and independent
C) are always mutually exclusive
D) are always independent

Question 31

Events A and B are mutually exclusive if their joint probability is

A) larger than 1
B) less than zero
C) zero
D) infinity

Question 32

An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is

A) 16
B) 8
C) 4
D) 2

Question 33

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 3 customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is

A) 2
B) 4
C) 6
D) 8

Question 34

If PA) = 0.4, PB | A) = 0.35, PA ∪ B) = 0.69, then PB) =

A) 0.14
B) 0.43
C) 0.75
D) 0.59

Question 35

Assume your favorite football team has 2 games left to finish the season. The outcome of each game can be win, lose or tie. The number of possible outcomes is

A) 2
B) 4
C) 6
D) 9

Question 36

Given that event E has a probability of 0.31, the probability of the complement of event E

A) cannot be determined with the above information
B) can have any value between zero and one
C) 0.69
D) is 0.31

Question 37

Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is

A) much larger than one
B) zero
C) infinity
D) None of these alternatives is correct.

Question 38

If a dime is tossed four times and comes up tails all four times, the probability of heads on the fifth trial is

A) smaller than the probability of tails
B) larger than the probability of tails
C) 1/2
D) 1/32

Question 39

The set of all possible outcomes of an experiment is

A) an experiment
B) an event
C) the population
D) the sample space

Question 40

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

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

Question 41

If A and B are independent events with PA) = 0.05 and PB) = 0.65, then PA | B) =

A) 0.05
B) 0.0325
C) 0.65
D) 0.8

Question 42

Bayes' theorem is used to compute

A) the prior probabilities
B) the union of events
C) intersection of events
D) the posterior probabilities

Question 43

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

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

Question 44

If PA) = 0.5 and PB) = 0.5, then PA ∩ B)

A) is 0.00
B) is 1.00
C) is 0.5
D) None of these alternatives is correct.

Question 45

If two events are independent, then

A) they must be mutually exclusive
B) the sum of their probabilities must be equal to one
C) their intersection must be zero
D) None of these alternatives is correct.

Question 46

If A and B are mutually exclusive events with PA) = 0.3 and PB) = 0.5, then PA ∩ B) =

A) 0.30
B) 0.15
C) 0.00
D) 0.20

Question 47

Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is

A) 0.25
B) 0.50
C) 1.00
D) 0.75

Question 48

If a coin is tossed three times, the likelihood of obtaining three heads in a row is

A) zero
B) 0.500
C) 0.875
D) 0.125

Question 49

If two events are mutually exclusive, then their intersection

A) will be equal to zero
B) can have any value larger than zero
C) must be larger than zero, but less than one
D) will be one

Question 50

If A and B are mutually exclusive events with PA) = 0.4 and PB) = 0.45, then PA ∪ B) =

A) 0.00
B) 0.15
C) 0.95
D) 0.2

Question 51

The union of two events with nonzero probabilities

A) cannot be less than one
B) cannot be one
C) could be larger than one
D) None of these alternatives is correct.

Question 52

On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and "cold" weather is .15. Are snow and "cold" weather independent events?

A) only if given that it snowed
B) no
C) yes
D) only when they are also mutually exclusive

Question 53

The union of events A and B is the event containing

A) all the sample points belonging to B or A
B) all the sample points belonging to A or B
C) all the sample points belonging to A or B or both
D) all the sample points belonging to A or B, but not both

Question 54

A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is

A) 30
B) 100
C) 729
D) 1,000

Question 55

If A and B are independent events with PA) = 0.4 and PB) = 0.6, then PA ∩ B) =

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

Question 56

The symbol ∩ shows the

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

Question 57

The symbol ∪ shows the

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

Question 58

One of the basic requirements of probability is

A) for each experimental outcome Ei, we must have PEi) ≥ 1
B) PA) = PAc) - 1
C) if there are k experimental outcomes, then ∑PEi) = 1
D) ∑PEi) ≥ 1

Question 59

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

A) zero
B) 1/16
C) 1/2
D) larger than the probability of tails

Question 60

If A and B are independent events with PA) = 0.2 and PB) = 0.6, then PA ∪ B) =

A) 0.62
B) 0.12
C) 0.60
D) 0.68

Question 61

If X and Y are mutually exclusive events with PX) = 0.295, PY) = 0.32, then PX | Y) =

A) 0.0944
B) 0.6150
C) 1.0000
D) 0.0000

Question 62

A perfectly balanced coin is tossed 6 times and tails appears on all six tosses. Then, on the seventh trial

A) tails can not appear
B) heads has a larger chance of appearing than tails
C) tails has a better chance of appearing than heads
D) None of these alternatives is correct.

Question 63

In an experiment, events A and B are mutually exclusive. If PA) = 0.6, then the probability of B

A) cannot be larger than 0.4
B) can be any value greater than 0.6
C) can be any value between 0 to 1
D) cannot be determined with the information given

Question 64

A six-sided die is tossed 3 times. The probability of observing three ones in a row is

A) 1/3
B) 1/6
C) 1/27
D) 1/216

Question 65

An experiment consists of four outcomes with PE1) = 0.2, PE2) = 0.3, and PE3) = 0.4. The probability of outcome E4 is

A) 0.500
B) 0.024
C) 0.100
D) 0.900

Question 66

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

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

Question 67

A method of assigning probabilities based on historical data is called the

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

Question 68

Events A and B are mutually exclusive. Which of the following statements is also true?

A) A and B are also independent.
B) PA ∪ B) = PA)PB)
C) PA ∪ B) = PA) + PB)
D) PA ∩ B) = PA) + PB)

Question 69

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

A) smaller than the probability of tails
B) larger than the probability of tails
C) 1/16
D) 1/2

Question 70

If PA) = 0.68, PA ∪ B) = 0.91, and PA ∩ B) = 0.35, then PB) =

A) 0.22
B) 0.09
C) 0.65
D) 0.58

Question 71

The set of all possible sample points experimental outcomes) is called

A) a sample
B) an event
C) the sample space
D) a population

Question 72

The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed 2 times and event A did not occur, then on the third trial event A

A) must occur
B) may occur
C) could not occur
D) has a 2/3 probability of occurring

Question 73

Events A and B are mutually exclusive with PA) = 0.3 and PB) = 0.2. Then, PBc) =

A) 0.00
B) 0.06
C) 0.7
D) 0.8

Question 74

If PA) = 0.62, PB) = 0.47, and PA ∪ B) = 0.88, then PA ∩ B) =

A) 0.2914
B) 1.9700
C) 0.6700
D) 0.2100

Question 75

If A and B are independent events with PA) = 0.4 and PB) = 0.25, then PA ∪ B) =

A) 0.65
B) 0.55
C) 0.10
D) 0.75

Question 76

If A and B are independent events with PA) = 0.38 and PB) = 0.55, then PA | B) =

A) 0.209
B) 0.000
C) 0.550
D) 0.38

Question 77

The probability assigned to each experimental outcome must be

A) any value larger than zero
B) smaller than zero
C) at least one
D) between zero and one

Question 78

If PA) = 0.58, PB) = 0.44, and PA ∩ B) = 0.25, then PA ∪ B) =

A) 1.02
B) 0.77
C) 0.11
D) 0.39

Question 79

If PA) = 0.50, PB) = 0.60, and PA ∩ B) = 0.30, then events A and B are

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

Question 80

If PA) = 0.50, PB) = 0.40, then, and PA ∪ B) = 0.88, then PB | A) =

A) 0.02
B) 0.03
C) 0.04
D) 0.05