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7. Suppose that you are dealt a hand of 9 cards from a standard deck of 52 playing cards.

a. What is the probability that you are dealt exactly 3 kings?

b. What is the probability that you are dealt 9 cards of the same suit?

c. What is the probability that you are not dealt at least 2 cards of each suit?

11. In how many ways can the letters in the word POSSESSIONS be arranged?

a. In how many ways can they be arranged if the first letter must be an S and the last letter must be an E?

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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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