Question 1

Determine whether the given events A and B are independent.   ,   , and   . Answer dependent or independent.

Accepted Answer

independent

Question 2

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram.   Find P(Dc) and P(B|Dc).
If necessary, round your answer to two decimal places.
P(Dc) = __________
P(B|Dc) = __________

Accepted Answer

0.45; 0.33

Question 3

Based on data obtained from the National Institute of Dental Research, it has been determined that 44% of 12-year-olds have never had a cavity, 35% of 13-year-olds have never had a cavity, and 25% of 14-year-olds have never had a cavity. If a child is selected at random from a group of 20 junior high school students comprising four 12-year-olds, six 13-year-olds, and ten 14-year-olds and this child does not have a cavity, what is the probability that this child is 14 years old?

Accepted Answer

A)  0.67 
B)  0.04 
C)  0.39 
D)  0.3 
A)  0.67 
B)  0.04 
C)  0.39 
D)  0.3 C

Question 4

An insurance company has compiled the accompanying data relating the age of drivers and the accident rate (the probability of being involved in an accident during a 1-year period) for drivers within that group:   
a. What is the probability that an insured driver will be involved in an accident during a particular 1-year period? If necessary, round your answer to two decimal places.
__________
b. What is the probability that an insured driver who is involved in an accident is under 25? If necessary, round your answer to two decimal places.
__________

Accepted Answer

The answer of An insurance company has compiled the accompanying...

Question 5

Let   be a sample space of an experiment and let   , and   be events of this experiment. ​
Find the events E ∪ F and E ∩ F.
​

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Let S be any sample space and N, F, and E be any three events associated with the experiment. Describe the following event, using the symbols ∪, ∩, and c. ​
The event that E does not occur.
​

Accepted Answer

A)  Ec 
B)    
C)    
D)    
E)    
A)  Ec 
B)    
C)    
D)    
E)

Question 7

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the sum of the numbers falling uppermost is greater than or equal to 7.

Accepted Answer

A)  {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} 
B)  {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)} 
C)  {(1, 6), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 3), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} 
D)  Ø 
A)  {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} 
B)  {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)} 
C)  {(1, 6), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 3), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} 
D)  Ø

Question 8

An experiment consists of selecting a card at random from a 52-card deck. Find the probability of the event that a club or a queen is drawn. Give the answer as a fraction.

Accepted Answer

The answer of An experiment consists of selecting a card...

Question 9

Eight players, A, B, C, D, E, F, G, and H, are competing in a series of elimination matches of a tennis tournament in which the winner of each preliminary match will advance to the semifinals and the winner of the semifinals will advance to the finals. An outline of the scheduled matches follows. Describe a sample space listing the possible participants in the finals.

Accepted Answer

A)  S = {(A,
D) , (A,F), (A,H), (C,
B) , (C,F), (C,H), (E,
B) , (E,
D) , (E, H), (G,
B) ,
(G,
D) , (G,F)} 
B)  S = {(A,
B) , (A,
D) , (A,F), (A,H), (C,
B) , (C,
D) , (C,F), (C,H), (E,
B) , (E,
D) ,
(E,F), (E, H), (G,
B) , (G,
D) , (G,F), (G,H)} 
C)  S = {(A,
E) , (A,F), (A,G), (A,H), (B,
E) , (B,F), (B,G), (B,H), (C, 
E) , (C,F),
(C,G), (C,H), (D,
E) , (D,F), (D,G), (D,H)} 
D)  S = {(A,
B) , (A,
C) , (A,
D) , (B,С), (B,
D) , (C,
D) , (E,F), (E,G), (E, H), (F,G),
(F,H), (G,H)} 
E)  None of the above. 
A)  S = {(A,
D) , (A,F), (A,H), (C,
B) , (C,F), (C,H), (E,
B) , (E,
D) , (E, H), (G,
B) ,
(G,
D) , (G,F)} 
B)  S = {(A,
B) , (A,
D) , (A,F), (A,H), (C,
B) , (C,
D) , (C,F), (C,H), (E,
B) , (E,
D) ,
(E,F), (E, H), (G,
B) , (G,
D) , (G,F), (G,H)} 
C)  S = {(A,
E) , (A,F), (A,G), (A,H), (B,
E) , (B,F), (B,G), (B,H), (C, 
E) , (C,F),
(C,G), (C,H), (D,
E) , (D,F), (D,G), (D,H)} 
D)  S = {(A,
B) , (A,
C) , (A,
D) , (B,С), (B,
D) , (C,
D) , (E,F), (E,G), (E, H), (F,G),
(F,H), (G,H)} 
E)  None of the above.

Question 10

Let S = {s1, s2, s3, s4, s5, s6} be the sample space associated with an experiment having the following probability distribution:   
 ​
Find the probability of the event A = {s1, s3}.

Accepted Answer

Question 11

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. ​   ​
Find   .
​

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

Urn A contains eight white and four black balls. Urn B contains seven white and three black balls. A ball is drawn from urn A and then transferred to urn B. A ball is then drawn from urn B. What is the probability that the transferred ball was black given that the second ball drawn was white?

Accepted Answer

A)  0.3 
B)  0.72 
C)  0.58 
D)  0.9 
A)  0.3 
B)  0.72 
C)  0.58 
D)  0.9

Question 13

An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event "A head is tossed and an even number is rolled."

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Let   ,   ,   and   .
Find the event E ∪ F ∪ G.
Express your answer using set notation.

Accepted Answer

The answer of Let   ,   ,...

Question 15

Two light bulbs are selected at random from a lot of 26, of which 4 are defective. What is the probability that at least 1 of the light bulbs is defective?

Accepted Answer

A)  0.943 
B)  0.174 
C)  0.256 
D)  0.047 
E)  0.289
F) 0.008 
A)  0.943 
B)  0.174 
C)  0.256 
D)  0.047 
E)  0.289
F) 0.008

Question 16

A pair of dice is cast, and the number that appears uppermost on each die is observed. Find the probability of the event that one die shows a 6, and the other is a number less than 4.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the sample space S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Determine the event that the number falling uppermost on one die is a 4 and the number falling uppermost on the other die is less than 4.

Accepted Answer

A)  {(1, 4), (2, 4), (3, 4), (4, 3), (4, 2), (4, 1)} 
B)  {(4, 5), (4, 6), (5, 2), (6, 4)} 
C)  {(2, 3), (2, 4), (6, 5), (2, 6), (3, 2), (4, 2), (5, 1), (6, 2)} 
D)  Ø 
A)  {(1, 4), (2, 4), (3, 4), (4, 3), (4, 2), (4, 1)} 
B)  {(4, 5), (4, 6), (5, 2), (6, 4)} 
C)  {(2, 3), (2, 4), (6, 5), (2, 6), (3, 2), (4, 2), (5, 1), (6, 2)} 
D)  Ø

Question 18

Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a heart given that the second card is a clubs?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram.
​   ​
Find P(Dc) and P(B|Dc).
​
If necessary, round your answer to two decimal places.
​
P(Dc) = __________
​
P(B|Dc) = __________

Accepted Answer

The answer of An experiment in which the three mutually...

Question 20

An experiment consists of selecting a card at random from a 52-card deck. Find the probability of the event that an ace is not drawn. Give the answer as a fraction.

Accepted Answer

The answer of An experiment consists of selecting a card...

Determine whether the given events A and B are independent. , , and . Answer dependent or independent.

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. Find P(Dc) and P(B|Dc). If necessary, round your answer to two decimal places. P(Dc) = P(B|Dc) =

Let be a sample space of an experiment and let , and be events of this experiment. Find the events E ∪ F and E ∩ F.

Let S be any sample space and N, F, and E be any three events associated with the experiment. Describe the following event, using the symbols ∪, ∩, and ^c. The event that E does not occur.

An experiment consists of selecting a card at random from a 52-card deck. Find the probability of the event that a club or a queen is drawn. Give the answer as a fraction.

Let S = {s₁, s₂, s₃, s₄, s₅, s₆} be the sample space associated with an experiment having the following probability distribution: Find the probability of the event A = {s₁, s₃}.

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. Find .

Urn A contains eight white and four black balls. Urn B contains seven white and three black balls. A ball is drawn from urn A and then transferred to urn B. A ball is then drawn from urn B. What is the probability that the transferred ball was black given that the second ball drawn was white?

An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event "A head is tossed and an even number is rolled."

Let , , and . Find the event E ∪ F ∪ G. Express your answer using set notation.

Two light bulbs are selected at random from a lot of 26, of which 4 are defective. What is the probability that at least 1 of the light bulbs is defective?

A pair of dice is cast, and the number that appears uppermost on each die is observed. Find the probability of the event that one die shows a 6, and the other is a number less than 4.

Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a heart given that the second card is a clubs?

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. Find P(Dc) and P(B|Dc). If necessary, round your answer to two decimal places. P(Dc) = P(B|Dc) =

An experiment consists of selecting a card at random from a 52-card deck. Find the probability of the event that an ace is not drawn. Give the answer as a fraction.

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Exam 7: Probability

Determine whether the given events A and B are independent. , , and . Answer dependent or independent.

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. Find P(Dc) and P(B|Dc). If necessary, round your answer to two decimal places. P(Dc) = __________ P(B|Dc) = __________

Let be a sample space of an experiment and let , and be events of this experiment. ​ Find the events E ∪ F and E ∩ F. ​

Let S be any sample space and N, F, and E be any three events associated with the experiment. Describe the following event, using the symbols ∪, ∩, and c. ​ The event that E does not occur. ​

An experiment consists of selecting a card at random from a 52-card deck. Find the probability of the event that a club or a queen is drawn. Give the answer as a fraction.

Let S = {s1, s2, s3, s4, s5, s6} be the sample space associated with an experiment having the following probability distribution: ​ Find the probability of the event A = {s1, s3}.

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. ​ ​ Find . ​

Urn A contains eight white and four black balls. Urn B contains seven white and three black balls. A ball is drawn from urn A and then transferred to urn B. A ball is then drawn from urn B. What is the probability that the transferred ball was black given that the second ball drawn was white?

An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event "A head is tossed and an even number is rolled."

Let , , and . Find the event E ∪ F ∪ G. Express your answer using set notation.

Two light bulbs are selected at random from a lot of 26, of which 4 are defective. What is the probability that at least 1 of the light bulbs is defective?

A pair of dice is cast, and the number that appears uppermost on each die is observed. Find the probability of the event that one die shows a 6, and the other is a number less than 4.

Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a heart given that the second card is a clubs?

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. ​ ​ Find P(Dc) and P(B|Dc). ​ If necessary, round your answer to two decimal places. ​ P(Dc) = __________ ​ P(B|Dc) = __________

An experiment consists of selecting a card at random from a 52-card deck. Find the probability of the event that an ace is not drawn. Give the answer as a fraction.

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. Find P(Dc) and P(B|Dc). If necessary, round your answer to two decimal places. P(Dc) = P(B|Dc) =

Let be a sample space of an experiment and let , and be events of this experiment. Find the events E ∪ F and E ∩ F.

Let S be any sample space and N, F, and E be any three events associated with the experiment. Describe the following event, using the symbols ∪, ∩, and ^c. The event that E does not occur.

Let S = {s₁, s₂, s₃, s₄, s₅, s₆} be the sample space associated with an experiment having the following probability distribution: Find the probability of the event A = {s₁, s₃}.

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. Find .

An experiment in which the three mutually exclusive events, A, B, and C form a partition of the uniform sample space S is depicted in the diagram. Find P(Dc) and P(B|Dc). If necessary, round your answer to two decimal places. P(Dc) = P(B|Dc) =