Three coins are tossed. a. Give an example of a simple event . b. Give an example of a joint event. c. What is the complement of a head on the first toss? d. what does the sample space consist of?

Question

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Answer 1

Textbook Question

Chapter 4, Problem 1PS

Three coins are tossed.

a. Give an example of a simple event.

b. Give an example of a joint event.

c. What is the complement of a head on the first toss?

d. what does the sample space consist of?

a.

Expert Solution

To determine

Determine an example of a simple event when three coins are tossed.

Answer to Problem 1PS

Simple events are tossing the heads or tossing a tail

Explanation of Solution

A simple event is an event that has only one characteristic, that is, it contains the outcomes that cannot be further subdivided.

An example of a simple event, when a coin is tossed, is either getting a head or getting a tail. These outcomes represent one characteristics, and it cannot be further subdivided.

b.

Expert Solution

To determine

Determine an example of a joint event when three coins are tossed.

Answer to Problem 1PS

Joint events are tossing three heads, tossing three tail etcetera.

Explanation of Solution

Joint Event is an event that has two or more characteristics. Joint probability is the likelihood of more than one event occurring at the same time.

An example of a joint event can be simultaneously tossing three heads HHH ,or a tail followed by two heads THH or a head followed by two tails HTT or simultaneously tossing three tails TTT . All these events have more than one characteristic, and it can be further subdivided.

c.

Expert Solution

To determine

Determine the complement of an event â€˜head on the first tossâ€™.

Answer to Problem 1PS

The complement of head is getting a tail.

Explanation of Solution

Complement is the subset of outcomes that are not a part of the event.

When a coin is tossed twice, there are two possible outcomes which are getting a head or getting a tail. Both these events are mutually exclusive and exhaustive events.

Therefore, if the head comes up, tail canâ€™t and vice versa. So, the complement of a head on the first toss will be tail coming on the first toss.

d.

Expert Solution

To determine

Determine the sample space on tossing three coins.

Explanation of Solution

Sample Space is the set of all possible outcomes. So, the sample space of tossing three coins will consist of 8 outcomes which are: HHH,HHT,HTH,THH,TTH,THT,HTT,TTT

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Answer 2

Textbook Question

Chapter 4, Problem 1PS

Three coins are tossed.

a. Give an example of a simple event.

b. Give an example of a joint event.

c. What is the complement of a head on the first toss?

d. what does the sample space consist of?

a.

Expert Solution

To determine

Determine an example of a simple event when three coins are tossed.

Answer to Problem 1PS

Simple events are tossing the heads or tossing a tail

Explanation of Solution

A simple event is an event that has only one characteristic, that is, it contains the outcomes that cannot be further subdivided.

An example of a simple event, when a coin is tossed, is either getting a head or getting a tail. These outcomes represent one characteristics, and it cannot be further subdivided.

b.

Expert Solution

To determine

Determine an example of a joint event when three coins are tossed.

Answer to Problem 1PS

Joint events are tossing three heads, tossing three tail etcetera.

Explanation of Solution

Joint Event is an event that has two or more characteristics. Joint probability is the likelihood of more than one event occurring at the same time.

An example of a joint event can be simultaneously tossing three heads HHH ,or a tail followed by two heads THH or a head followed by two tails HTT or simultaneously tossing three tails TTT . All these events have more than one characteristic, and it can be further subdivided.

c.

Expert Solution

To determine

Determine the complement of an event â€˜head on the first tossâ€™.

Answer to Problem 1PS

The complement of head is getting a tail.

Explanation of Solution

Complement is the subset of outcomes that are not a part of the event.

When a coin is tossed twice, there are two possible outcomes which are getting a head or getting a tail. Both these events are mutually exclusive and exhaustive events.

Therefore, if the head comes up, tail canâ€™t and vice versa. So, the complement of a head on the first toss will be tail coming on the first toss.

d.

Expert Solution

To determine

Determine the sample space on tossing three coins.

Explanation of Solution

Sample Space is the set of all possible outcomes. So, the sample space of tossing three coins will consist of 8 outcomes which are: HHH,HHT,HTH,THH,TTH,THT,HTT,TTT

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Answer 3

Textbook Question

Chapter 4, Problem 1PS

Three coins are tossed.

a. Give an example of a simple event.

b. Give an example of a joint event.

c. What is the complement of a head on the first toss?

d. what does the sample space consist of?

a.

Expert Solution

To determine

Determine an example of a simple event when three coins are tossed.

Answer to Problem 1PS

Simple events are tossing the heads or tossing a tail

Explanation of Solution

A simple event is an event that has only one characteristic, that is, it contains the outcomes that cannot be further subdivided.

An example of a simple event, when a coin is tossed, is either getting a head or getting a tail. These outcomes represent one characteristics, and it cannot be further subdivided.

b.

Expert Solution

To determine

Determine an example of a joint event when three coins are tossed.

Answer to Problem 1PS

Joint events are tossing three heads, tossing three tail etcetera.

Explanation of Solution

Joint Event is an event that has two or more characteristics. Joint probability is the likelihood of more than one event occurring at the same time.

An example of a joint event can be simultaneously tossing three heads HHH ,or a tail followed by two heads THH or a head followed by two tails HTT or simultaneously tossing three tails TTT . All these events have more than one characteristic, and it can be further subdivided.

c.

Expert Solution

To determine

Determine the complement of an event â€˜head on the first tossâ€™.

Answer to Problem 1PS

The complement of head is getting a tail.

Explanation of Solution

Complement is the subset of outcomes that are not a part of the event.

When a coin is tossed twice, there are two possible outcomes which are getting a head or getting a tail. Both these events are mutually exclusive and exhaustive events.

Therefore, if the head comes up, tail canâ€™t and vice versa. So, the complement of a head on the first toss will be tail coming on the first toss.

d.

Expert Solution

To determine

Determine the sample space on tossing three coins.

Explanation of Solution

Sample Space is the set of all possible outcomes. So, the sample space of tossing three coins will consist of 8 outcomes which are: HHH,HHT,HTH,THH,TTH,THT,HTT,TTT

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Answer 4

Textbook Question

Chapter 4, Problem 1PS

Three coins are tossed.

a. Give an example of a simple event.

b. Give an example of a joint event.

c. What is the complement of a head on the first toss?

d. what does the sample space consist of?

a.

Expert Solution

To determine

Determine an example of a simple event when three coins are tossed.

Answer to Problem 1PS

Simple events are tossing the heads or tossing a tail

Explanation of Solution

A simple event is an event that has only one characteristic, that is, it contains the outcomes that cannot be further subdivided.

An example of a simple event, when a coin is tossed, is either getting a head or getting a tail. These outcomes represent one characteristics, and it cannot be further subdivided.

b.

Expert Solution

To determine

Determine an example of a joint event when three coins are tossed.

Answer to Problem 1PS

Joint events are tossing three heads, tossing three tail etcetera.

Explanation of Solution

Joint Event is an event that has two or more characteristics. Joint probability is the likelihood of more than one event occurring at the same time.

An example of a joint event can be simultaneously tossing three heads HHH ,or a tail followed by two heads THH or a head followed by two tails HTT or simultaneously tossing three tails TTT . All these events have more than one characteristic, and it can be further subdivided.

c.

Expert Solution

To determine

Determine the complement of an event â€˜head on the first tossâ€™.

Answer to Problem 1PS

The complement of head is getting a tail.

Explanation of Solution

Complement is the subset of outcomes that are not a part of the event.

When a coin is tossed twice, there are two possible outcomes which are getting a head or getting a tail. Both these events are mutually exclusive and exhaustive events.

Therefore, if the head comes up, tail canâ€™t and vice versa. So, the complement of a head on the first toss will be tail coming on the first toss.

d.

Expert Solution

To determine

Determine the sample space on tossing three coins.

Explanation of Solution

Sample Space is the set of all possible outcomes. So, the sample space of tossing three coins will consist of 8 outcomes which are: HHH,HHT,HTH,THH,TTH,THT,HTT,TTT

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

Determine an example of a simple event when three coins are tossed.

Answer to Problem 1PS

Simple events are tossing the heads or tossing a tail

Explanation of Solution

A simple event is an event that has only one characteristic, that is, it contains the outcomes that cannot be further subdivided.

An example of a simple event, when a coin is tossed, is either getting a head or getting a tail. These outcomes represent one characteristics, and it cannot be further subdivided.

b.

Expert Solution

To determine

Determine an example of a joint event when three coins are tossed.

Answer to Problem 1PS

Joint events are tossing three heads, tossing three tail etcetera.

Explanation of Solution

Joint Event is an event that has two or more characteristics. Joint probability is the likelihood of more than one event occurring at the same time.

An example of a joint event can be simultaneously tossing three heads HHH ,or a tail followed by two heads THH or a head followed by two tails HTT or simultaneously tossing three tails TTT . All these events have more than one characteristic, and it can be further subdivided.

c.

Expert Solution

To determine

Determine the complement of an event â€˜head on the first tossâ€™.

Answer to Problem 1PS

The complement of head is getting a tail.

Explanation of Solution

Complement is the subset of outcomes that are not a part of the event.

When a coin is tossed twice, there are two possible outcomes which are getting a head or getting a tail. Both these events are mutually exclusive and exhaustive events.

Therefore, if the head comes up, tail canâ€™t and vice versa. So, the complement of a head on the first toss will be tail coming on the first toss.

d.

Expert Solution

To determine

Determine the sample space on tossing three coins.

Explanation of Solution

Sample Space is the set of all possible outcomes. So, the sample space of tossing three coins will consist of 8 outcomes which are: HHH,HHT,HTH,THH,TTH,THT,HTT,TTT

Answer 8

a.

Expert Solution

To determine

Determine an example of a simple event when three coins are tossed.

Answer to Problem 1PS

Simple events are tossing the heads or tossing a tail

Explanation of Solution

A simple event is an event that has only one characteristic, that is, it contains the outcomes that cannot be further subdivided.

An example of a simple event, when a coin is tossed, is either getting a head or getting a tail. These outcomes represent one characteristics, and it cannot be further subdivided.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Determine an example of a simple event when three coins are tossed.

Answer 13

Answer to Problem 1PS

Simple events are tossing the heads or tossing a tail

Answer 14

Explanation of Solution

A simple event is an event that has only one characteristic, that is, it contains the outcomes that cannot be further subdivided.

An example of a simple event, when a coin is tossed, is either getting a head or getting a tail. These outcomes represent one characteristics, and it cannot be further subdivided.

Answer 15

b.

Expert Solution

To determine

Determine an example of a joint event when three coins are tossed.

Answer to Problem 1PS

Joint events are tossing three heads, tossing three tail etcetera.

Explanation of Solution

Joint Event is an event that has two or more characteristics. Joint probability is the likelihood of more than one event occurring at the same time.

An example of a joint event can be simultaneously tossing three heads HHH ,or a tail followed by two heads THH or a head followed by two tails HTT or simultaneously tossing three tails TTT . All these events have more than one characteristic, and it can be further subdivided.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Determine an example of a joint event when three coins are tossed.

Answer 20

Answer to Problem 1PS

Joint events are tossing three heads, tossing three tail etcetera.

Answer 21

Explanation of Solution

Joint Event is an event that has two or more characteristics. Joint probability is the likelihood of more than one event occurring at the same time.

An example of a joint event can be simultaneously tossing three heads HHH ,or a tail followed by two heads THH or a head followed by two tails HTT or simultaneously tossing three tails TTT . All these events have more than one characteristic, and it can be further subdivided.

Answer 22

c.

Expert Solution

To determine

Determine the complement of an event â€˜head on the first tossâ€™.

Answer to Problem 1PS

The complement of head is getting a tail.

Explanation of Solution

Complement is the subset of outcomes that are not a part of the event.

When a coin is tossed twice, there are two possible outcomes which are getting a head or getting a tail. Both these events are mutually exclusive and exhaustive events.

Therefore, if the head comes up, tail canâ€™t and vice versa. So, the complement of a head on the first toss will be tail coming on the first toss.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Determine the complement of an event â€˜head on the first tossâ€™.

Answer 27

Answer to Problem 1PS

The complement of head is getting a tail.

Answer 28

Explanation of Solution

Complement is the subset of outcomes that are not a part of the event.

When a coin is tossed twice, there are two possible outcomes which are getting a head or getting a tail. Both these events are mutually exclusive and exhaustive events.

Therefore, if the head comes up, tail canâ€™t and vice versa. So, the complement of a head on the first toss will be tail coming on the first toss.

Answer 29

d.

Expert Solution

To determine

Determine the sample space on tossing three coins.

Explanation of Solution

Sample Space is the set of all possible outcomes. So, the sample space of tossing three coins will consist of 8 outcomes which are: HHH,HHT,HTH,THH,TTH,THT,HTT,TTT

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

Determine the sample space on tossing three coins.

Answer 34

Explanation of Solution

Sample Space is the set of all possible outcomes. So, the sample space of tossing three coins will consist of 8 outcomes which are: HHH,HHT,HTH,THH,TTH,THT,HTT,TTT