Deck 4: Introduction to Probability

Question 1

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

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

Answer 1

subjective

Question 2

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

Answer 2

classical

Question 3

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 3

the sample space.

Question 4

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 5

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 6

Each individual outcome of an experiment is called

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

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 counting rule for

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

Question 8

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 9

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 10

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 11

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 12

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 13

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 14

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

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

Question 15

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 16

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 17

Events that have no sample points in common are

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

Question 18

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

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

Question 19

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 20

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 21

The symbol ∪ shows the

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

Question 22

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 23

The symbol ∩ shows the

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

Question 24

Bayes' theorem is used to compute

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

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

Question 26

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 27

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 28

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 29

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 30

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 31

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 32

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 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

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 35

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 36

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 37

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 38

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 39

The sum of the probabilities of two complementary events is

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

Question 40

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 41

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 42

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 43

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

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

Question 44

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 45

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 46

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 47

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 48

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 49

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 50

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 51

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 52

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 53

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 54

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 55

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 56

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 57

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 58

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 59

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 60

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 61

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 62

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 63

Posterior probabilities are computed using

A) the Multiplication Law.
B) Chebyshev's theorem.
C) the empirical rule.
D) Bayes' theorem.

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

An element of the sample space is

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

Question 66

The complement of P(A | B) is

A) P(A^C | B).
B) P(A | B^C).
C) P(B | A).
D) P(A  B).

Question 67

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 68

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 69

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 70

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 71

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 72

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 73

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

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

Question 74

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 75

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 76

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 77

The probability of an intersection of two events is computed using the _____ law.

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

Question 78

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 79

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 80

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