Obtain the sample space for the event B c .

Question

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Answer 1

Question

Chapter 6.1, Problem 13E

a.

To determine

Obtain the sample space for the event Bc.

a.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

The given information is that there are three people in a family and each person P1, P2 and P3 in the family are assigned to stations 1, 2 and 3.

Sample Space:

A sample space is the set of all possible outcomes of a random experiment.

Here, there are three persons in a family and each person is assigned to three stations.

The 27 possible outcomes are as follows:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2), (1,2,3),(1,3,1),(1,3,2),(1,3,3),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,1),(3,1,2),(3,1,3),(3,2,1),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

It is given that the event B is all three people go to different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Complement of an event A is the set of all outcomes that are not in A. It is denoted as Ac.

P(Ac)=1−P(A)

The event Bc denotes the set of all outcomes that are not in B.

Therefore, the sample space for the event Bc is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

b.

To determine

Obtain the sample space for the event Cc.

b.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

Then the event Cc denotes the set of all outcomes that are not in C.

Therefore, the sample space for the event Cc is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

c.

To determine

Obtain the sample space for the event A∪B.

c.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3),(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∪B contains all the outcomes in A and B.

Therefore, the sample space for the event A∪B is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

d.

To determine

Obtain the sample space for the event A∩B.

d.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space=ϕ.

Explanation of Solution

Calculation:

It is given that the event A is all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different station.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∩B contains the outcomes that are common in both A and B. There is no outcomes that are common in both A and B.

Therefore, the sample space for the event A∩B is given by:

Sample space=ϕ.

e.

To determine

Obtain the sample space for the event A∩C.

e.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three person are assigned to station 1 or three person are assigned to station 2 or three person are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

The sample space for the event A∩C contains the outcomes that are common in both A and B. The outcomes that are common in both A and B are (1,1,1) and. (3,3,3).

Therefore, the sample space for the event A∩C is given by:

Sample space={(1,1,1),(3,3,3)}.

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Answer 2

Question

Chapter 6.1, Problem 13E

a.

To determine

Obtain the sample space for the event Bc.

a.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

The given information is that there are three people in a family and each person P1, P2 and P3 in the family are assigned to stations 1, 2 and 3.

Sample Space:

A sample space is the set of all possible outcomes of a random experiment.

Here, there are three persons in a family and each person is assigned to three stations.

The 27 possible outcomes are as follows:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2), (1,2,3),(1,3,1),(1,3,2),(1,3,3),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,1),(3,1,2),(3,1,3),(3,2,1),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

It is given that the event B is all three people go to different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Complement of an event A is the set of all outcomes that are not in A. It is denoted as Ac.

P(Ac)=1−P(A)

The event Bc denotes the set of all outcomes that are not in B.

Therefore, the sample space for the event Bc is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

b.

To determine

Obtain the sample space for the event Cc.

b.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

Then the event Cc denotes the set of all outcomes that are not in C.

Therefore, the sample space for the event Cc is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

c.

To determine

Obtain the sample space for the event A∪B.

c.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3),(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∪B contains all the outcomes in A and B.

Therefore, the sample space for the event A∪B is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

d.

To determine

Obtain the sample space for the event A∩B.

d.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space=ϕ.

Explanation of Solution

Calculation:

It is given that the event A is all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different station.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∩B contains the outcomes that are common in both A and B. There is no outcomes that are common in both A and B.

Therefore, the sample space for the event A∩B is given by:

Sample space=ϕ.

e.

To determine

Obtain the sample space for the event A∩C.

e.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three person are assigned to station 1 or three person are assigned to station 2 or three person are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

The sample space for the event A∩C contains the outcomes that are common in both A and B. The outcomes that are common in both A and B are (1,1,1) and. (3,3,3).

Therefore, the sample space for the event A∩C is given by:

Sample space={(1,1,1),(3,3,3)}.

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Answer 3

Question

Chapter 6.1, Problem 13E

a.

To determine

Obtain the sample space for the event Bc.

a.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

The given information is that there are three people in a family and each person P1, P2 and P3 in the family are assigned to stations 1, 2 and 3.

Sample Space:

A sample space is the set of all possible outcomes of a random experiment.

Here, there are three persons in a family and each person is assigned to three stations.

The 27 possible outcomes are as follows:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2), (1,2,3),(1,3,1),(1,3,2),(1,3,3),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,1),(3,1,2),(3,1,3),(3,2,1),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

It is given that the event B is all three people go to different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Complement of an event A is the set of all outcomes that are not in A. It is denoted as Ac.

P(Ac)=1−P(A)

The event Bc denotes the set of all outcomes that are not in B.

Therefore, the sample space for the event Bc is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

b.

To determine

Obtain the sample space for the event Cc.

b.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

Then the event Cc denotes the set of all outcomes that are not in C.

Therefore, the sample space for the event Cc is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

c.

To determine

Obtain the sample space for the event A∪B.

c.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3),(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∪B contains all the outcomes in A and B.

Therefore, the sample space for the event A∪B is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

d.

To determine

Obtain the sample space for the event A∩B.

d.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space=ϕ.

Explanation of Solution

Calculation:

It is given that the event A is all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different station.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∩B contains the outcomes that are common in both A and B. There is no outcomes that are common in both A and B.

Therefore, the sample space for the event A∩B is given by:

Sample space=ϕ.

e.

To determine

Obtain the sample space for the event A∩C.

e.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three person are assigned to station 1 or three person are assigned to station 2 or three person are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

The sample space for the event A∩C contains the outcomes that are common in both A and B. The outcomes that are common in both A and B are (1,1,1) and. (3,3,3).

Therefore, the sample space for the event A∩C is given by:

Sample space={(1,1,1),(3,3,3)}.

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Answer 4

Question

Chapter 6.1, Problem 13E

a.

To determine

Obtain the sample space for the event Bc.

a.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

The given information is that there are three people in a family and each person P1, P2 and P3 in the family are assigned to stations 1, 2 and 3.

Sample Space:

A sample space is the set of all possible outcomes of a random experiment.

Here, there are three persons in a family and each person is assigned to three stations.

The 27 possible outcomes are as follows:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2), (1,2,3),(1,3,1),(1,3,2),(1,3,3),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,1),(3,1,2),(3,1,3),(3,2,1),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

It is given that the event B is all three people go to different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Complement of an event A is the set of all outcomes that are not in A. It is denoted as Ac.

P(Ac)=1−P(A)

The event Bc denotes the set of all outcomes that are not in B.

Therefore, the sample space for the event Bc is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

b.

To determine

Obtain the sample space for the event Cc.

b.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

Then the event Cc denotes the set of all outcomes that are not in C.

Therefore, the sample space for the event Cc is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

c.

To determine

Obtain the sample space for the event A∪B.

c.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3),(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∪B contains all the outcomes in A and B.

Therefore, the sample space for the event A∪B is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

d.

To determine

Obtain the sample space for the event A∩B.

d.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space=ϕ.

Explanation of Solution

Calculation:

It is given that the event A is all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different station.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∩B contains the outcomes that are common in both A and B. There is no outcomes that are common in both A and B.

Therefore, the sample space for the event A∩B is given by:

Sample space=ϕ.

e.

To determine

Obtain the sample space for the event A∩C.

e.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three person are assigned to station 1 or three person are assigned to station 2 or three person are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

The sample space for the event A∩C contains the outcomes that are common in both A and B. The outcomes that are common in both A and B are (1,1,1) and. (3,3,3).

Therefore, the sample space for the event A∩C is given by:

Sample space={(1,1,1),(3,3,3)}.

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Answer 5

Chapter 6.1, Problem 13E

a.

To determine

Obtain the sample space for the event Bc.

a.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

The given information is that there are three people in a family and each person P1, P2 and P3 in the family are assigned to stations 1, 2 and 3.

Sample Space:

A sample space is the set of all possible outcomes of a random experiment.

Here, there are three persons in a family and each person is assigned to three stations.

The 27 possible outcomes are as follows:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2), (1,2,3),(1,3,1),(1,3,2),(1,3,3),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,1),(3,1,2),(3,1,3),(3,2,1),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

It is given that the event B is all three people go to different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Complement of an event A is the set of all outcomes that are not in A. It is denoted as Ac.

P(Ac)=1−P(A)

The event Bc denotes the set of all outcomes that are not in B.

Therefore, the sample space for the event Bc is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

b.

To determine

Obtain the sample space for the event Cc.

b.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

Then the event Cc denotes the set of all outcomes that are not in C.

Therefore, the sample space for the event Cc is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

c.

To determine

Obtain the sample space for the event A∪B.

c.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3),(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∪B contains all the outcomes in A and B.

Therefore, the sample space for the event A∪B is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

d.

To determine

Obtain the sample space for the event A∩B.

d.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space=ϕ.

Explanation of Solution

Calculation:

It is given that the event A is all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different station.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∩B contains the outcomes that are common in both A and B. There is no outcomes that are common in both A and B.

Therefore, the sample space for the event A∩B is given by:

Sample space=ϕ.

e.

To determine

Obtain the sample space for the event A∩C.

e.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three person are assigned to station 1 or three person are assigned to station 2 or three person are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

The sample space for the event A∩C contains the outcomes that are common in both A and B. The outcomes that are common in both A and B are (1,1,1) and. (3,3,3).

Therefore, the sample space for the event A∩C is given by:

Sample space={(1,1,1),(3,3,3)}.

Answer 6

Chapter 6.1, Problem 13E

a.

To determine

Obtain the sample space for the event Bc.

a.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

The given information is that there are three people in a family and each person P1, P2 and P3 in the family are assigned to stations 1, 2 and 3.

Sample Space:

A sample space is the set of all possible outcomes of a random experiment.

Here, there are three persons in a family and each person is assigned to three stations.

The 27 possible outcomes are as follows:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2), (1,2,3),(1,3,1),(1,3,2),(1,3,3),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,1),(3,1,2),(3,1,3),(3,2,1),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

It is given that the event B is all three people go to different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Complement of an event A is the set of all outcomes that are not in A. It is denoted as Ac.

P(Ac)=1−P(A)

The event Bc denotes the set of all outcomes that are not in B.

Therefore, the sample space for the event Bc is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Answer 7

Chapter 6.1, Problem 13E

a.

To determine

Obtain the sample space for the event Bc.

Answer 8

a.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation:

The given information is that there are three people in a family and each person P1, P2 and P3 in the family are assigned to stations 1, 2 and 3.

Sample Space:

A sample space is the set of all possible outcomes of a random experiment.

Here, there are three persons in a family and each person is assigned to three stations.

The 27 possible outcomes are as follows:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2), (1,2,3),(1,3,1),(1,3,2),(1,3,3),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,1),(3,1,2),(3,1,3),(3,2,1),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

It is given that the event B is all three people go to different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Complement of an event A is the set of all outcomes that are not in A. It is denoted as Ac.

P(Ac)=1−P(A)

The event Bc denotes the set of all outcomes that are not in B.

Therefore, the sample space for the event Bc is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Answer 13

b.

To determine

Obtain the sample space for the event Cc.

b.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

Then the event Cc denotes the set of all outcomes that are not in C.

Therefore, the sample space for the event Cc is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

Answer 14

b.

To determine

Obtain the sample space for the event Cc.

Answer 15

b.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(1,1,2),(1,1,3),(1,2,1),(1,2,2),(1,3,1),(1,3,3),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(2,2,3),(2,3,2),(2,3,3),(3,1,1),(3,1,3),(3,2,2),(3,2,3),(3,3,1),(3,3,2),(3,3,3)}.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Calculation:

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

Then the event Cc denotes the set of all outcomes that are not in C.

Therefore, the sample space for the event Cc is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

Answer 20

c.

To determine

Obtain the sample space for the event A∪B.

c.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3),(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∪B contains all the outcomes in A and B.

Therefore, the sample space for the event A∪B is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

Answer 21

c.

To determine

Obtain the sample space for the event A∪B.

Answer 22

c.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3),(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different stations.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∪B contains all the outcomes in A and B.

Therefore, the sample space for the event A∪B is given by:

Sample space={(1,1,2),(1,2,1),(1,2,2), (1,2,3),(1,3,2),(2,1,1),(2,1,2),(2,1,3),(2,2,1),(2,2,2),(2,2,3),(2,3,1),(2,3,2),(2,3,3),(3,1,2),(3,2,1),(3,2,2),(3,2,3),(3,3,2)}.

Answer 27

d.

To determine

Obtain the sample space for the event A∩B.

d.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space=ϕ.

Explanation of Solution

Calculation:

It is given that the event A is all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different station.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∩B contains the outcomes that are common in both A and B. There is no outcomes that are common in both A and B.

Therefore, the sample space for the event A∩B is given by:

Sample space=ϕ.

Answer 28

d.

To determine

Obtain the sample space for the event A∩B.

Answer 29

d.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space=ϕ.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Calculation:

It is given that the event A is all three people go to the same station.

Then the possibilities for event A are either three persons are assigned to station 1 or three persons are assigned to station 2 or three persons are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event B is that all three people go to the different station.

Therefore, the sample space for the event B is given by:

Sample space={(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)}.

The sample space for the event A∩B contains the outcomes that are common in both A and B. There is no outcomes that are common in both A and B.

Therefore, the sample space for the event A∩B is given by:

Sample space=ϕ.

Answer 34

e.

To determine

Obtain the sample space for the event A∩C.

e.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(3,3,3)}.

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three person are assigned to station 1 or three person are assigned to station 2 or three person are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

The sample space for the event A∩C contains the outcomes that are common in both A and B. The outcomes that are common in both A and B are (1,1,1) and. (3,3,3).

Therefore, the sample space for the event A∩C is given by:

Sample space={(1,1,1),(3,3,3)}.

Answer 35

e.

To determine

Obtain the sample space for the event A∩C.

Answer 36

e.

Expert Solution

Answer to Problem 13E

The sample space of possible outcomes is given by:

Sample space={(1,1,1),(3,3,3)}.

Answer 37

e.

Expert Solution

Answer 38

e.

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Calculation:

It is given that the event A is that all three people go to the same station.

Then the possibilities for event A are either three person are assigned to station 1 or three person are assigned to station 2 or three person are assigned to station 3.

Therefore, the sample space for A is given by:

Sample space={(1,1,1),(2,2,2),(3,3,3)}.

It is given that the event C is that no one goes to station.

Therefore, the sample space for the event C is given by:

Sample space={(1,1,1),(1,1,3),(1,3,1),(1,3,3),(3,1,1),(3,1,3),(3,3,1),(3,3,3)}.

The sample space for the event A∩C contains the outcomes that are common in both A and B. The outcomes that are common in both A and B are (1,1,1) and. (3,3,3).