Deck 4: Introduction to Probability

Question 1

The range of probability is _____,

A) any value larger than 0
B) any value between minus infinity to plus infinity
C) 0 to 1, inclusive
D) any value between -1 to 1

Answer 1

0 to 1, inclusive

Question 2

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

Answer 2

the sample space

Question 3

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)

Answer 3

P(A^c | B)

Question 4

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 5

Twenty percent of people at a company picnic got food poisoning. What percent of the people at the picnic did NOT get food poisoning?

A) 20%
B) 40%
C) 60%
D) 80%

Question 6

An element of the sample space is a(n) _____.

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

Question 7

Posterior probabilities are computed using _____.

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

Question 8

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 9

The sample space refers to _____.

A) any particular experimental outcome
B) the sample size minus 1
C) the set of all possible experimental outcomes
D) both any particular experimental outcome and the set of all possible experimental outcome

Question 10

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

A) .33
B) .50
C) .75
D) 1

Question 11

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 12

Since the sun MUST rise tomorrow, then the probability of the sun rising tomorrow is _____.

A) much larger than 1
B) 0
C) infinity
D) None of the answers is correct.

Question 13

Posterior probabilities are _____.

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

Question 14

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 the answers are correct.

Question 15

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

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

Question 16

Revised probabilities of events based on additional information are _____.

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

Question 17

There is a 60% chance of getting stuck in traffic when leaving the city. On two separate days, what is the probability that you get stuck in traffic both days?

A) .36
B) .60
C) 1.20
D) .30

Question 18

Suppose we flip a fair coin five times and each time it lands heads up. The probability of landing heads up on the next flip is _____.

A) 1/2
B) 1
C) 0
D) None of the answers is correct.

Question 19

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 20

Any process that generates well-defined outcomes is _____.

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

Question 21

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

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

Question 22

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 23

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following three 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 24

Given that event E has a probability of .25, the probability of the complement of event E _____.

A) cannot be determined with the above information
B) can have any value between 0 and 1
C) must be .75
D) is .25

Question 25

A professor rolls a fair, six-sided die. Using the classical method of probability, what is the probability that at least three spots will be showing up on the die?

A) 1/2
B) 2/3
C) 1/3
D) 1/6

Question 26

The symbol ∪ indicates the _____.

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

Question 27

A magician holds a standard deck of cards and draws one card. The probability of drawing the ace of diamonds is 1/52. What method of assigning probabilities was used?

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

Question 28

Assume your favorite football team has two 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

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 30

The probability of the union of two events with nonzero probabilities _____.

A) cannot be less than 1
B) cannot be 1
C) cannot be less than one and cannot be 1
D) None of the answers is correct.

Question 31

An experiment consists of four outcomes with P(E₁) = .2, P(E₂) = .3, and P(E₃) = .4. The probability of outcome E₄ is _____.

A) .500
B) .024
C) .100
D) .900

Question 32

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 33

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 34

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 35

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

A) bar chart
B) tree diagram
C) histogram
D) None of the answers is correct.

Question 36

A graphical method of representing the sample points of a multiple-step experiment is a(n) _____.

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

Question 37

A __________ 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 38

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

A) .25
B) .50
C) 1
D) .75

Question 39

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 40

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

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

Question 41

If A and B are mutually exclusive events with P(A) = .3 and P(B) = .5, then P(A ∪ B) =

A) 0
B) .15
C) .8
D) .2

Question 42

If A and B are independent events with P(A) = .38 and P(B) = .55, then P(A | B) =

A) .209
B) 0
C) .550
D) None of the answers is correct.

Question 43

The symbol ∩ shows the _____.

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

Question 44

If P(A) = .62, P(B) = .56, and P(A ∪ B) = .70, then P(B | A) = _____.

A) .4800
B) .7742
C) .9032
D) Not enough information is given to answer this question.

Question 45

If P(A) = .75, P(A ∪ B) = .86, and P(A ∩ B) = .56, then P(B) =

A) .25
B) .67
C) .56
D) .11

Question 46

If P(A) = .62, P(B) = .47, and P(A ∪ B) = .88; then P(A ∩ B) =

A) .291
B) 1.970
C) .670
D) .210

Question 47

The probability of the intersection of two mutually exclusive events _____.

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

Question 48

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) 1
B) any positive value
C) 0
D) any value between 0 and 1

Question 49

If P(A) = .38, P(B) = .83, and P(A ∩ B) = .24; then P(A ∪ B) =

A) 1.21
B) .97
C) .76
D) 1.45

Question 50

In an experiment, events A and B are mutually exclusive. If P(A) = .6, then the probability of B _____.

A) cannot be larger than .4
B) can be any value greater than .6
C) can be any value between 0 and 1
D) cannot be determined with the information given

Question 51

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 .5
D) the probability of their intersection is 1 and they have no sample points in common

Question 52

Events A and B are mutually exclusive with P(A) = .3 and P(B) = .2. The probability of the complement of event B equals _____.

A) 0
B) .06
C) .70
D) None of the answers is correct.

Question 53

If two events are mutually exclusive, then the probability of their intersection _____.

A) will be equal to 0
B) can have any value larger than 0
C) must be larger than zero, but less than 1
D) will be 1

Question 54

If two events are independent, then _____.

A) they must be mutually exclusive
B) the sum of their probabilities must be equal to 1
C) the probability of their intersection must be 0
D) None of the answers is correct.

Question 55

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 answers is correct.

Question 56

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) both P(A) = 1 − P(A^c) and P(A) + P(B) = 1

Question 57

You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common.

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

Question 58

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 59

One of the basic requirements of probability is _____.

A) for each experimental outcome E_i, we must have P(E_i) ≥ 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 60

If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A ∩ B) =

A) .30
B) .15
C) 0
D) .20

Question 61

A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl?

A) .125
B) .5
C) .875
D) 1

Question 62

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 63

If A and B are independent events with P(A) = .2 and P(B) = .6, then P(A ∪ B) = _____.

A) .62
B) .12
C) .60
D) .68

Question 64

If A and B are independent events with P(A) = .4 and P(B) = .25, then P(A ∪ B) = _____.

A) .65
B) .55
C) .10
D) Not enough information is given to answer this question.

Question 65

The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed two 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 66

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 67

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

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

Question 68

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 69

If P(A) = .50, P(B) = .60, and P(A ∩ B) = .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 70

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

A) 0
B) 1/32
C) 1/2
D) 1/5

Question 71

If P(A ∩ 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 72

A six-sided die is rolled three times. The probability of observing a 1 three times in a row is _____.

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

Question 73

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

A) 0
B) .500
C) .875
D) .125

Question 74

If X and Y are mutually exclusive events with P(X) = .295, P(Y) = .32, then P(X ∪ Y) = _____.

A) .094
B) .615
C) 1
D) 0

Question 75

If P(A) = .5 and P(B) = .5, then P(A ∩ B) _____.

A) is 0
B) is .25
C) is 1
D) cannot be determined from the information given

Question 76

If a fair 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 answers is correct.

Question 77

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 78

If A and B are independent events with P(A) = .4 and P(B) = .6, then P(A ∩ B) = _____.

A) .76
B) 1
C) .24
D) .2

Question 79

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) are always independent

Question 80

If A and B are independent events with P(A) = .05 and P(B) = .65, then P(A | B) = _____.

A) .05
B) .0325
C) .65
D) .8