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What is Probability?

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Define probability and explain its three perspectives. Can you also provide an example of each.

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What is probability?
- Probability deals with chance. It is a measure of the likelihood of an event happening given a certain number of tries. Generally speaking you can say that probability is represented on a percentage scale. In statistics however, it is most likely to be represented by a decimal number that falls somewhere between and including 0 and 1. So for example a 2% chance would be written as 0.02 probability, while a 20% chance would be written as 0.2 probability. (Fractions are also common).
- The closer you are to 0, the less likely it is that the event being considered will happen. The closer you are to 1, the event then has a higher chance or probability of happening.

Important terms in the study of probability:
- Experiment: "a process that leads to the occurrence of one and only one of several possible observations" (Lind, Marchal, & Wathen, 2008) For example, if you have 5 peanut M&M's left in ...

Solution Summary

This solution examines the three perspectives of probability.

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A young engineer has invented holographic mobile phones and has approached a venture capital company to invest in it. The venture capital company considers the product to be an all or nothing product: either everyone will want one because everyone else has one or no one will want one because there will be no one to use it with. The company believes that the probability that it will take off netting them a profit of $2000000 is 0.14. If it doesn't take off then they expect that they would loose $200000. They are considering using a consumer survey to gather more information. However, the company has experience that shows that the probability that the consumer survey will predict success for a product that will fail is 0.24, and the probability that the consumer survey will predict failure when the product will be a success is 0.07. What is the monetary value of the information from a consumer survey to the venture capital company in this case? (ie what is the maximum that they should spend on a consumer survey)?

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