Deck 4: Introduction to Probability

Question 1

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

A) stacked bar chart.
B) dot plot.
C) stem-and-leaf display.
D) tree diagram.

Answer 1

tree diagram.

Question 2

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.

Answer 2

relative frequency method.

Question 3

Each individual outcome of an experiment is called

A) the sample space.
B) a sample point.
C) a trial.
D) an event.

Answer 3

a sample point.

Question 4

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 5

The collection of all possible sample points in an experiment is

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

Question 6

Any process that generates well-defined outcomes is

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

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 important is called the

A) counting rule for permutations.
B) counting rule for combinations.
C) counting rule for independent events.
D) counting rule for multiple-step random experiments.

Question 8

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.

Question 9

The intersection of two mutually exclusive events

A) can be any value between 0 to1.
B) must always be equal to 1.
C) must always be equal to 0.
D) can be any positive value.

Question 10

The range of probability is

A) 0 to infinity.
B) minus infinity to plus infinity.
C) 0 to 1.
D) -1 to 1.

Question 11

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 12

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 the

A) counting rule for permutations.
B) counting rule for combinations.
C) counting rule for independent events.
D) counting rule for multiple-step experiments.

Question 13

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 might occur.
D) a different out come must occur.

Question 14

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 15

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 16

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 17

Events that have no sample points in common are

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

Question 18

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

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

Question 19

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) if most of their sample points are in common.

Question 20

Initial estimates of the probabilities of events are known as

A) subjective probabilities.
B) posterior probabilities.
C) conditional probabilities.
D) prior probabilities.

Question 21

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

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

Question 22

The symbol ∩ shows the

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

Question 23

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 24

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

A) 0.0.
B) 0.500.
C) 0.875.
D) 0.125.

Question 25

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 26

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 27

The union of events A and B is the event containing all the sample points belonging to

A) B or A.
B) A or B.
C) A or B or both.
D) A or B, but not both.

Question 28

Assume your favorite soccer 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 29

If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =

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

Question 30

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 31

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) the product of their probabilities gives their intersection.

Question 32

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

A) 0.
B) 1/16.
C) 1/2.
D) larger than the probability of tails.

Question 33

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 34

The sum of the probabilities of two complementary events is

A) 0.
B) 0.5.
C) 0.57.
D) 1.0.

Question 35

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 36

Bayes' theorem is used to compute

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

Question 37

The symbol ∪ shows the

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

Question 38

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

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

Question 39

The set of all possible outcomes of an experiment is

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

Question 40

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 41

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 42

If P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88, then P(A ∩ B) =

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

Question 43

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 ∪ B) = P(A)P(B)
C) P(A ∪ B) = P(A) + P(B)
D) P(A ∩ B) = P(A) + P(B)

Question 44

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

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

Question 45

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 46

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

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

Question 47

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

A) tail can not appear.
B) head has a larger chance of appearing than tail.
C) tail has a better chance of appearing than head.
D) tail has same chance of appearing as the head.

Question 48

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 49

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 50

Events A and B are mutually exclusive with P(C) = 0.3 and P(B) = 0.2.Then, P(B^c) =

A) 0.06.
B) 0.50.
C) 0.70.
D) 0.80.

Question 51

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

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

Question 52

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

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

Question 53

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 54

If A and B are independent events with P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B)

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

Question 55

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

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

Question 56

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

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

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

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 59

If P(A) = 0.58, P(B) = 0.44, and P(A ∩ B) = 0.25, then P(A ∪ B) =

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

Question 60

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

A) 0.00.
B) 0.15.
C) 0.80.
D) 0.20.

Question 61

Some of the CDs produced by a manufacturer are defective.From the production line, 5 CDs are selected and inspected.How many sample points exist in this experiment?

A) 10
B) 25
C) 30
D) 32

Question 62

If X and Y are mutually exclusive events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =

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

Question 63

Posterior probabilities are​​

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

Question 64

If P(A) = 0.45, P(B) = 0.55, and P(A ∪ B) = 0.78, then P(A | B) =

A) 0.00
B) 0.45
C) 0.22
D) 0.40

Question 65

If P(A) = 0.48, P(A ∪ B) = 0.82, and P(B) = 0.54, then P(A ∩ B) =

A) 0.3936.
B) 0.3400.
C) 0.2000.
D) 1.0200.

Question 66

​An element of the sample space is

A) ​an event.
B) ​an experiment.
C) ​a sample point.
D) ​a permutation.

Question 67

The complement of P(A | B) is​

A) ​P(A^C | B).
B) ​P(A | B^C).
C) ​P(B | A).
D) ​P(A I B).

Question 68

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

A) ​0.25.
B) ​0.33.
C) ​0.50.
D) ​0.75.

Question 69

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

A) 0.209.
B) 0.000.
C) 0.550.
D) 0.380.

Question 70

From nine cards numbered 1 through 9, two cards are drawn.Consider the selection and classification of the cards as odd or even as an experiment.How many sample points are there for this experiment?

A) 2
B) 3
C) 4
D) 9

Question 71

​Revised probabilities of events based on additional information are

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

Question 72

If P(A) = 0.50, P(B) = 0.40 and P(A ∪ B) = 0.88, then P(B |A) =

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

Question 73

If A and B are mutually exclusive, then​

A) ​P(A) + P(B) = 0.
B) ​P(A) + P(B) = 1.
C) ​P(A ∩ B) = 0.
D) ​P(A ∩ B) = 1.

Question 74

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

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

Question 75

Assume your favorite soccer team has 3 games left to finish the season.The outcome of each game can be win, lose, or tie.How many possible outcomes exist?

A) 7
B) 27
C) 36
D) 64

Question 76

Each customer entering a department store will either buy or not buy some merchandise.An experiment consists of following 4 customers and determining whether or not they purchase any merchandise.How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)

A) 2
B) 4
C) 12
D) 16

Question 77

Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female.How many sample points exist in the above experiment?

A) 64
B) 32
C) 16
D) 4

Question 78

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 79

If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are

A) non-mutually exclusive.
B) mutually exclusive.
C) independent events.
D) complements of each other.

Question 80

​Posterior probabilities are computed using

A) ​relative frequency.
B) ​Chebyshev's theorem.
C) ​the empirical rule.
D) ​Bayes' theorem.