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Chapter 7: Problem 80

Let \(E\) be the event that you buy a Porsche. Which of the following could reasonably represent the experiment and sample space in question? (A) You go to an auto dealership and select a Mustang; \(S\) is the set of colors available. (B) You go to an auto dealership and select a red car; \(S\) is the set of cars you decide not to buy. (C) You go to an auto dealership and select a red car; \(S\) is the set of car models available.

Short Answer

Expert verified
The most appropriate representation for the experiment and sample space related to the event of buying a Porsche is option (C). In this option, the experiment is going to an auto dealership and selecting a red car, and the sample space (S) is the set of car models available, which could potentially include a Porsche.

Step by step solution

01

Understand the Event

The event (E) is the act of buying a Porsche. Therefore, we need to find an option that best describes an experiment where the decision to buy a Porsche is related to the sample space.
02

Option A Analysis

In this option, the experiment is going to an auto dealership and selecting a Mustang. The sample space (S) is the set of colors available. This option doesn't involve Porsche, so it doesn't represent the given event.
03

Option B Analysis

Here, the experiment is going to an auto dealership and selecting a red car. The sample space (S) is the set of cars that you decide not to buy. This option doesn't give us any information about whether the Porsche is being considered or not. Thus, it also doesn't represent the event in question.
04

Option C Analysis

In this option, the experiment is going to an auto dealership and selecting a red car. The sample space (S) is the set of car models available. Since the sample space consists of car models, it's possible that a Porsche could be among those models being considered. This option has the potential to relate to the event of buying a Porsche.
05

Conclusion

Based on the analysis, option (C) is the most reasonable choice for representing the experiment and sample space related to the event of buying a Porsche.

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