Homework Help is Here – Start Your Trial Now!
Math
Probability
EXAMPLE 2.1 A contractor is planning the acquisition of construction equipment, including bulldozers, needed for a new project in a remote area. Suppose that from his prior experience with similar bulldozers, he estimated that there is a 50% chance that each bulldozer can remain operational for at least 6 months. If he purchased three bulldozers for the new project, what is the probability that there will be only 1 bulldozer left operational after 6 months into the project? First, we observe that at the end of 6 months, the possible number of operating bulldozers will be 0, 1, 2, or 3; therefore, this set of numbers constitute the possibility space of the number of operational bulldozers after 6 months. However, this possibility space is not pertinent to the question referred to above. For this latter purpose, the possibility space must be derived from the possible status of each bulldozer after 6 months, as follows: Denoting the condition of each bulldozer after 6 months as O for operational and N for nonope- rational, the possible conditions of the three bulldozers would be: 000 all three bulldozers are operational OON first and second bulldozers are operational, whereas the third one is nonoperational ONN NNN-all three bulldozers are nonoperational NOO

EXAMPLE 2.1 A contractor is planning the acquisition of construction equipment, including bulldozers, needed for a new project in a remote area. Suppose that from his prior experience with similar bulldozers, he estimated that there is a 50% chance that each bulldozer can remain operational for at least 6 months. If he purchased three bulldozers for the new project, what is the probability that there will be only 1 bulldozer left operational after 6 months into the project? First, we observe that at the end of 6 months, the possible number of operating bulldozers will be 0, 1, 2, or 3; therefore, this set of numbers constitute the possibility space of the number of operational bulldozers after 6 months. However, this possibility space is not pertinent to the question referred to above. For this latter purpose, the possibility space must be derived from the possible status of each bulldozer after 6 months, as follows: Denoting the condition of each bulldozer after 6 months as O for operational and N for nonope- rational, the possible conditions of the three bulldozers would be: 000 all three bulldozers are operational OON first and second bulldozers are operational, whereas the third one is nonoperational ONN NNN-all three bulldozers are nonoperational NOO

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question
This subject is Engineering data analysis.
28 Chapter 2. Fundamentals of Probability Models NNO ONO NON Therefore, the pertinent possibility space consists of the eight possible outcomes as indicated above. We observe also that since the condition of a bulldozer is equally likely to be operational or nonoperational after 6 months, the eight possible outcomes are equally likely to occur. It is also worth noting that among the eight possible outcomes, only one of them can be realized at the end of 6 months; this means that the different possibilities are mutually exclusive (we shall say more on this point in Section 2.2.1). Finally, among the eight possible outcomes, the realization of ONN, NON, or NNO is tantamount to the event of interest, namely, "only one bulldozer is operational." Because each possible outcome is equally likely to occur, the probability of the event within the above possibility space is 3/8.
Transcribed Image Text:28 Chapter 2. Fundamentals of Probability Models NNO ONO NON Therefore, the pertinent possibility space consists of the eight possible outcomes as indicated above. We observe also that since the condition of a bulldozer is equally likely to be operational or nonoperational after 6 months, the eight possible outcomes are equally likely to occur. It is also worth noting that among the eight possible outcomes, only one of them can be realized at the end of 6 months; this means that the different possibilities are mutually exclusive (we shall say more on this point in Section 2.2.1). Finally, among the eight possible outcomes, the realization of ONN, NON, or NNO is tantamount to the event of interest, namely, "only one bulldozer is operational." Because each possible outcome is equally likely to occur, the probability of the event within the above possibility space is 3/8.
► EXAMPLE 2.1 A contractor is planning the acquisition of construction equipment, including bulldozers, needed for a new project in a remote area. Suppose that from his prior experience with similar bulldozers, he estimated that there is a 50% chance that each bulldozer can remain operational for at least 6 months. If he purchased three bulldozers for the new project, what is the probability that there will be only 1 bulldozer left operational after 6 months into the project? First, we observe that at the end of 6 months, the possible number of operating bulldozers will be 0, 1, 2, or 3; therefore, this set of numbers constitute the possibility space of the number of operational bulldozers after 6 months. However, this possibility space is not pertinent to the question referred to above. For this latter purpose, the possibility space must be derived from the possible status of each bulldozer after 6 months, as follows: Denoting the condition of each bulldozer after 6 months as O for operational and N for nonope- rational, the possible conditions of the three bulldozers would be: 000 all three bulldozers are operational OON first and second bulldozers are operational, whereas the third one is nonoperational ONN NNN-all three bulldozers are nonoperational NOO
Transcribed Image Text:► EXAMPLE 2.1 A contractor is planning the acquisition of construction equipment, including bulldozers, needed for a new project in a remote area. Suppose that from his prior experience with similar bulldozers, he estimated that there is a 50% chance that each bulldozer can remain operational for at least 6 months. If he purchased three bulldozers for the new project, what is the probability that there will be only 1 bulldozer left operational after 6 months into the project? First, we observe that at the end of 6 months, the possible number of operating bulldozers will be 0, 1, 2, or 3; therefore, this set of numbers constitute the possibility space of the number of operational bulldozers after 6 months. However, this possibility space is not pertinent to the question referred to above. For this latter purpose, the possibility space must be derived from the possible status of each bulldozer after 6 months, as follows: Denoting the condition of each bulldozer after 6 months as O for operational and N for nonope- rational, the possible conditions of the three bulldozers would be: 000 all three bulldozers are operational OON first and second bulldozers are operational, whereas the third one is nonoperational ONN NNN-all three bulldozers are nonoperational NOO
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS