28 Chapter 2. Fundamentals of Probability ModelsNNOONONONTherefore, the pertinent possibility space consists of the eight possible outcomes as indicatedabove. We observe also that since the condition of a bulldozer is equally likely to be operationalor nonoperational after 6 months, the eight possible outcomes are equally likely to occur. It is alsoworth noting that among the eight possible outcomes, only one of them can be realized at the end of6 months; this means that the different possibilities are mutually exclusive (we shall say more on thispoint in Section 2.2.1).Finally, among the eight possible outcomes, the realization of ONN, NON, or NNO is tantamountto the event of interest, namely, "only one bulldozer is operational." Because each possible outcomeis equally likely to occur, the probability of the event within the above possibility space is 3/8. ► EXAMPLE 2.1A contractor is planning the acquisition of construction equipment, including bulldozers, needed fora new project in a remote area. Suppose that from his prior experience with similar bulldozers, heestimated 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 only1 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 be0, 1, 2, or 3; therefore, this set of numbers constitute the possibility space of the number of operationalbulldozers after 6 months. However, this possibility space is not pertinent to the question referred toabove. For this latter purpose, the possibility space must be derived from the possible status of eachbulldozer 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 operationalOON first and second bulldozers are operational, whereas the third one is nonoperationalONNNNN-all three bulldozers are nonoperationalNOO

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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