Deck 4: Introduction to Probability

Question 1

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 the other answers is correct.

Answer 1

None of the other answers is correct.

Question 2

If A and B are mutually exclusive, then

A)P(A) + P(B) = 0
B)P(A) + P(B) = 1
C)P(AB) = 0
D)P(AB) = 1

Answer 2

P(AB) = 0

Question 3

Revised probabilities of events based on additional information are

A)joint probabilities
B)posterior probabilities
C)marginal probabilities
D)complementary probabilities

Answer 3

posterior probabilities

Question 4

Any process that generates well-defined outcomes is

A)an event
B)an experiment
C)a sample point
D)None of the other answers is correct.

Question 5

An element of the sample space is

A)an event
B)an estimator
C)a sample point
D)an outlier

Question 6

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 7

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 8

Three applications for admission to a local university are checked to determine 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 9

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 10

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 11

Posterior probabilities are computed using

A)the classical method
B)Chebyshev's theorem
C)the empirical rule
D)Bayes' theorem

Question 12

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 13

Posterior probabilities are

A)simple probabilities
B)marginal probabilities
C)joint probabilities
D)conditional probabilities

Question 14

The probability of an intersection of two events is computed using the

A)addition law
B)subtraction law
C)multiplication law
D)division law

Question 15

A sample point refers to a(n)

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)All of these answers are correct.

Question 16

The complement of P(A | B) is

A)P(A^C | B)
B)P(A | B^C)
C)P(B | A)
D)P(AB)

Question 17

Each individual outcome of an experiment is called

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

Question 18

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)both any particular experimental outcome and the set of all possible experimental outcomes are correct

Question 19

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)None of the other answers is correct.

Question 20

The probability of at least one head in two flips of a coin is

A)0.33
B)0.50
C)0.75
D)1.00

Question 21

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 22

The probability assigned to each experimental outcome must be

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

Question 23

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

A)relative method
B)probability method
C)classical method
D)None of the other answers is correct.

Question 24

The union of events A and B is the event containing

A)all the sample points common to both A and B
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 25

A graphical method of representing the sample points of a multiple-step experiment is

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

Question 26

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

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

Question 27

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 the other answers is correct.

Question 28

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 29

The probability of the union of two events with nonzero probabilities

A)cannot be less than one
B)cannot be one
C)cannot be less than one and cannot be one
D)None of the other answers is correct.

Question 30

The "Top Three" at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many "Top Three" outcomes are there?

A)302,400
B)720
C)1,814,400
D)10

Question 31

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 32

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)None of the other answers is correct.

Question 33

The symbol $\cup$ shows the

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

Question 34

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 35

Given that event E has a probability of 0.25, 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)must be 0.75
D)is 0.25

Question 36

A(n) __________ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles.

A)frequency polygon
B)histogram
C)Venn diagram
D)tree diagram

Question 37

The symbol $\cap$ shows the

A)union of events
B)intersection of events
C)sum of the probabilities of events
D)None of the other answers is correct.

Question 38

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 39

A(n) __________ is a collection of sample points.

A)probability
B)permutation
C)experiment
D)event

Question 40

An experiment consists of four outcomes with P(E₁) = 0.2, P(E₂) = 0.3, and P(E₃) = 0.4. The probability of outcome E₄ is

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

Question 41

If A and B are independent events with P(A) =0.38 and P(B) = 0.55, then P(A $\mid$ B) =

A)0.209
B)0.000
C)0.550
D)None of the other answers is correct.

Question 42

One of the basic requirements of probability is

A)for each experimental outcome E_i, we must have P(E_i) $\ge$ 1
B)P(A) = P(A^c) -1
C)if there are k experimental outcomes, then P(E₁) + P(E₂) + ... +P(E_k) = 1
D)both P(A) =P(A^c) - 1 and if there are k experimental outcomes, then P(E₁) + P(E₂) + ... + P(E_k) =1

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)None of the other answers is correct.

Question 44

If two events are mutually exclusive, then the probability of 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 45

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) =0.5, then P(A $\cap$ B) =

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

Question 46

If two events are independent, then

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

Question 47

Events A and B are mutually exclusive with P(A) =0.3 and P(B) =0.2. The probability of the complement of Event B equals

A)0.00
B)0.06
C)0.7
D)None of the other answers is correct.

Question 48

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A $\cup$ B) =

A)0.00
B)0.15
C)0.8
D)0.2

Question 49

Events that have no sample points in common are

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

Question 50

Which of the following statements is(are) always true?

A)-1 $\le$ P(E_i) $\le$ 1
B)P(A)= 1 - P(A^c)
C)P(A) + P(B) = 1
D)both P(A) =1 -P(A^c) and P(A) + P(B) = 1

Question 51

Two events, A and B, are mutually exclusive and each has 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 52

If X and Y are mutually exclusive events with P(X) =0.295, P(Y) =0.32, then P(X $\mid$ Y) =

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

Question 53

If P(A) =0.62, P(B) = 0.47, and P(A $\cup$ B) = 0.88; then P(A $\cap$ B) =

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

Question 54

Two events are mutually exclusive if

A)the probability of their intersection is 1
B)they have no sample points in common
C)the probability of their intersection is 0.5
D)the probability of their intersection is 1 and they have no sample points in common

Question 55

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 56

The probability of 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

Question 57

In an experiment, events A and B are mutually exclusive. If P(A) = 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 58

If P(A) =0.85, P(A $\cup$ B) = 0.72, and P(A $\cap$ B) = 0.66, then P(B) =

A)0.15
B)0.53
C)0.28
D)0.14

Question 59

If P(A)= 0.80, P(B) =0.65, and P(A $\cup$ B) = 0.78, then P(B $\mid$ A)=

A)0.6700
B)0.8375
C)0.9750
D)Not enough information is given to answer this question.

Question 60

If P(A) =0.38, P(B) = 0.83, and P(A $\cap$ B)=0.57; then P(A $\cup$ B) =

A)1.21
B)0.64
C)0.78
D)1.78

Question 61

On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and a "cold" day 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 62

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

A)0.76
B)1.00
C)0.24
D)0.2

Question 63

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)None of the other answers is correct.

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

Two events with nonzero probabilities

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

Question 66

If P(A) =0.5 and P(B) = 0.5, then P(A $\cap$ B) is

A)0.00
B)0.25
C)1.00
D)cannot be determined from the information given

Question 67

If P(A) =0.50, P(B) = 0.60, and P(A $\cap$ 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 68

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 69

The probability of an event is

A)the sum of the probabilities of the sample points in the event
B)the product of the probabilities of the sample points in the event
C)the minimum of the probabilities of the sample points in the event
D)the maximum of the probabilities of the sample points in the event

Question 70

If P(A $\cap$ B) = 0,

A)P(A) + P(B) = 1
B)either P(A) = 0 or P(B) = 0
C)A and B are mutually exclusive events
D)A and B are independent events

Question 71

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A $\cup$ B) =

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

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

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

A)zero
B)1/32
C)0.5
D)larger than the probability of tails

Question 74

If P(A|B) = .3,

A)P(B|A) = .7
B)P(A^C|B) = .7
C)P(A|B^C) = .7
D)P(A^C|B^C) = .7

Question 75

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

A)A and B are also independent.
B)P(A $\cup$ B) = P(A)P(B)
C)P(A $\cup$ B) = P(A) + P(B)
D)P(A $\cap$ B)= P(A) + P(B)

Question 76

If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A $\cup$ B) =

A)0.65
B)0.55
C)0.10
D)Not enough information is given to answer this question.

Question 77

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

A)tails cannot appear
B)heads has a larger chance of appearing than tails
C)tails has a better chance of appearing than heads
D)None of the other answers is correct.

Question 78

Bayes' theorem is used to compute

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

Question 79

If A and B are independent events with P(A)= 0.05 and P(B) = 0.65, then P(A $\mid$ B) =

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

Question 80

Initial estimates of the probabilities of events are known as

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