Question 1

If P(A)  = .85, P(B)  = .76, and P(A ? B)  = .72, then P(A | B)  = _____.

Accepted Answer

A)   .15
B)   .53
C)   .25
D)   .95E) None of the above
F) B) and C)

Question 2

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

Accepted Answer

A)   0
B)   .06
C)   .70
D)   None of the answers is correct.E) All of the above
F) B) and C)

Question 3

The symbol ∩ shows the _____.

Accepted Answer

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

Question 4

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

Accepted Answer

A)   16
B)   8
C)   4
D)   2E) A) and B)
F) A) and C)

Question 5

Two events are mutually exclusive if _____.

Accepted Answer

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 commonE) C) and D)
F) B) and D)

Question 6

The symbol ∪ indicates the _____.

Accepted Answer

A)   union of events
B)   intersection of events
C)   sum of the probabilities of events
D)   sample spaceE) None of the above
F) All of the above

Question 7

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

Accepted Answer

A)   frequency polygon
B)   histogram
C)   Venn diagram
D)   tree diagramE) None of the above
F) A) and B)

Question 8

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

Accepted Answer

A)   .30
B)   .15
C)   0
D)   .20E) A) and D)
F) A) and C)

Question 9

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

Accepted Answer

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 givenE) A) and D)
F) A) and C)

Question 10

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 _____.

Accepted Answer

A)   9
B)   14
C)   24
D)   36E) B) and C)
F) All of the above

Question 11

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

Accepted Answer

A)   0
B)   1/32
C)   1/2
D)   1/5E) All of the above
F) B) and C) C

Question 12

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

Accepted Answer

A)   .62
B)   .12
C)   .60
D)   .68E) A) and B)
F) All of the above

Question 13

If A and B are mutually exclusive, then _____.

Accepted Answer

A)   P(
A)   + P(
B)   = 0
B)   P(
A)   + P(
B)   = 1
C)   P(A ⋂ 
B)   = 0
D)   P(A ⋂ 
B)   = 1E) B) and C)
F) None of the above

Question 14

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.

Accepted Answer

A)   independent events
B)   posterior events
C)   mutually exclusive events
D)   complementsE) C) and D)
F) All of the above C

Question 15

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

Accepted Answer

A)   .500
B)   .024
C)   .100
D)   .900E) B) and C)
F) C) and D)

Question 16

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 _____.

Accepted Answer

A)   30
B)   100
C)   729
D)   1,000E) None of the above
F) B) and C)

Question 17

The multiplication law is potentially helpful when we are interested in computing the probability of _____.

Accepted Answer

A)   mutually exclusive events
B)   the intersection of two events
C)   the union of two events
D)   None of the answers is correct.E) None of the above
F) A) and B)

Question 18

If P(A | B)  = .3 and P(B)  = .8, then _____.

Accepted Answer

A)   P(
A)   = .24
B)   P(B | 
A)   = .7
C)   P(A ∩ 
B)   = .5
D)   P(A ∩ 
B)   = .24E) B) and D)
F) A) and B) D

Question 19

A sample point refers to a(n)  _____.

Accepted Answer

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.E) C) and D)
F) A) and B)

Question 20

One of the basic requirements of probability is _____.

Accepted Answer

A)   for each experimental outcome Ei, we must have P(Ei)  ≥ 1
B)   P(
A)   = P(Ac)  - 1
C)   if there are k experimental outcomes, then P(E1)  + P(E2)  + ... + P(Ek)  = 1
D)   both P(
A)   = P(Ac)  − 1 and if there are k experimental outcomes, then P(E1)  + P(E2)  + ... + P(Ek)  = 1E) B) and C)
F) A) and B)

Exam 4: Introduction to Probability

If P(A) = .85, P(B) = .76, and P(A ? B) = .72, then P(A | B) = _____.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

The symbol ∩ shows the _____.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Two events are mutually exclusive if _____.

Correct AnswerverifiedShow Answer

The symbol ∪ indicates the _____.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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 _____.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedC

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

Correct AnswerverifiedShow Answer

If A and B are mutually exclusive, then _____.

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedC

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

Correct AnswerverifiedShow Answer

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 _____.

Correct AnswerverifiedShow Answer

The multiplication law is potentially helpful when we are interested in computing the probability of _____.

Correct AnswerverifiedShow Answer

If P(A | B) = .3 and P(B) = .8, then _____.

Correct AnswerverifiedD

A sample point refers to a(n) _____.

Correct AnswerverifiedShow Answer

One of the basic requirements of probability is _____.

Correct AnswerverifiedShow Answer

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C

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C

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

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D

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