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Probability

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1. A cooler contains 100 cans of soda covered by ice. There are 30 cans of cola, 40 cans of orange soda, 10 cans of ginger ale, and 20 cans of root beer. The cans are all the same size and shape. If one can is selected at random from the cooler, determine the probability that the soda selected will be cola or orange.

2. Brain Teaser. A multiple- choice exam has four possible answers. For each correct answer you are awarded 5 points. For each incorrect answer 2 points are taken away from your score. For answers left blank no points are added or subtracted.

a) If you do not know the correct answer to a particular question, is it to your advantage to guess? Please explain your answer.
b)If you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? Please explain your answer.

3. Answer the following question. If a wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on a number greater than 6 given that the color is red. Hint. There are 3 red colors on the wheel with numbers 5,6,7. 2 green colors on the wheel with numbers 1,8. 5 purple colors on the wheel with numbers 2,4,9,11,12 and 2 brown colors on the wheel with numbers 3,10.

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This solution is comprised of a detailed step-by-step calculation and explanation of the various problems related to Probability. This solution provides students with a clear perspective of the given problems.

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The probability

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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