Deck 4: Introduction to Probability

Question 1

The collection of all possible sample points in an experiment is

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

Answer 1

the sample space.

Question 2

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.

Answer 2

if they have no sample points in common.

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

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 5

Initial estimates of the probabilities of events are known as _____ probabilities.

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

Question 6

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 rule for

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

Question 7

Events that have no sample points in common are

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

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

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 _____ method.

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

Question 10

Which of the following statements is always true?

A) -1 P(E_i) 1
B) P(A) = 1 - P(A^c)
C) P(A) + P(B) = 1
D) ∑P 1

Question 11

Any process that generates well-defined outcomes is a(n)

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

Question 12

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 13

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 14

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

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

Question 15

The range of probability values is

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

Question 16

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 17

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 18

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.

Question 19

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 counting rule for

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

Question 20

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

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

Question 21

Four 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) 16.
D) 8.

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

Bayes' theorem is used to compute

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

Question 24

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 25

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 26

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 card?

A) 1/52
B) 4/52
C) 13/52
D) 26/52

Question 27

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 28

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 29

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 30

If A and B are independent events with P(A) = 0.5 and P(A ∩ B) = 0.12, then, P(B) =

A) 0.240.
B) 0.060.
C) 0.380.
D) 0.620.

Question 31

The symbol ∩ shows the

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

Question 32

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 33

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 34

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

A) 10.
B) 625.
C) 150.
D) 180.

Question 35

Assume your favorite soccer team has 4 games left to finish the season.The outcome of each game can be win, lose or tie.The number of possible outcomes is

A) 4.
B) 12.
C) 64.
D) 81.

Question 36

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

A) 30
B) 11
C) 6!
D) 15

Question 37

The sum of the probabilities of two complementary events is

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

Question 38

Each customer entering a department store will either buy or not buy some merchandise.An experiment consists of following 5 customers and determining whether or not they purchase any merchandise.The number of sample points in this experiment is

A) 5.
B) 10.
C) 25.
D) 64.

Question 39

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 40

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) the same as any other outcome.
D) not able to be determined before the die is tossed.

Question 41

An experiment consists of four outcomes with P(E₁) = 0.2, P(E₂) = 0.25, and P(E₃) = 0.05.The probability of outcome E₄ is

A) 0.500.
B) 0.0025.
C) 0.100.
D) 0.

Question 42

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 43

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 44

A six-sided die is tossed 4times.The probability of observing four ones in a row is

A) 4/6.
B) 1/6.
C) 1/4096.
D) 1/1296.

Question 45

Of the last 100 customers entering a computer shop, 40have purchased a computer.If the classical method for computing probability is used, the probability that the next customer will purchase a computer is

A) 0.40.
B) 0.50.
C) 1.00.
D) 0.60.

Question 46

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

A) 0.00.
B) 1.00.
C) 0.5.
D) 0.25.

Question 47

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 48

Events A and B are mutually exclusive with P(C) = 0.35 and P(B) = 0.25.Then, P(B^c) =

A) 0.62.
B) 0.50.
C) 0.75.
D) 0.60.

Question 49

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

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

Question 50

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

A) 0.
B) 0.15.
C) 0.1.
D) 0.65.

Question 51

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 52

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 53

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 54

A lottery is conducted using four 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) 40.
B) 6,561.
C) 1,048,576.
D) 10,000.

Question 55

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 56

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 57

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

A) classical
B) subjective
C) relative frequency
D) progressive

Question 58

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 59

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) 0.1.
C) 0.625.
D) 0.15.

Question 60

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 61

A student has to take 12 more courses before he can graduate.If none of the courses are prerequisite to others, how many groups of four courses can he select for the next semester?

Question 62

From among 8 students how many committees consisting of 4 students can be selected?

Question 63

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 64

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 65

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

Question 66

Revised probabilities of events based on additional information are _____ probabilities.

A) joint
B) posterior
C) independent
D) complementary

Question 67

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 68

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 69

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 70

A college plans to interview 7 students for possible offer of graduate assistantships.The college has three assistantships available.How many groups of three can the college select?

Question 71

Six puppies were born in a litter, and it is determined whether each puppy is male or female.How many sample points exist in the above experiment?

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

Question 72

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 73

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 74

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 75

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.How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)

A) 3
B) 6
C) 8
D) 9

Question 76

Some of the CDs produced by a manufacturer are defective.From the production line, 4 CDs are selected and inspected.How many sample points exist in this experiment?

A) 4
B) 8
C) 16
D) 256

Question 77

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

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

Question 78

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 79

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 80

Twelve individuals are candidates for positions of president and vice president of an organization.How many possibilities of selections exist?