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Probability

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1. Of 23 college sophomores at Crocodile Community College, 12 preferred pepperoni pizza, 7 preferred supreme, and 4 preferred cheese. If we picked a college sophomore at Crocodile Community College at random, what is the probability that he or she would prefer supreme? Give solution exactly in reduced fraction form.

2. If the probability of seeing moose in a day in a certain region of Alaska is 0.29, what is the probability of not seeing any moose in a day there?

3. If the odds of winning a raffle are 7:229, what is the probability of winning?

4. According to the U. S. Census Bureau, the total 2008 U.S. population was 303,824,640. The chart below summarizes the 2008 population for five U.S. States.

U. S. State 2008 Population
Missouri 5,911,605
Pennsylvania 12,448,279
Tennessee 6,214,888
Utah 2,736,424
Washington 6,549,224

SOURCE: U. S. Census Bureau
What is the probability that a randomly selected U.S. resident did not live in Missouri? Show step by step work. Round solution to the nearest thousandth.

5. A simple dartboard has three areas... the main board has a radius of 10 inches, there is a circle with a radius of 7 inches, and the bullseye has a radius of 3 inches. What is the probability of a random dart landing inside the bullseye?

6. A certain drawing states that the odds of winning are 15:270. What would be the odds against winning?

7. The property restoration company PuroServ is considering switching to new dehumidifiers. Their market research, considering the cost of the new machines and their efficiency, tells them that the switch would give them a 72% chance of making a $20,000 profit, a 14% chance of breaking even, and a 14% chance of losing $5,000. How much money does PuroServ expect to make with their new purchase?

8. Last fall, a gardener planted 55 iris bulbs. She found that only 45 of the bulbs bloomed in the spring.
a. Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms.
b. How many of the bulbs should she plant next fall if she would like at least 51 to bloom?

9. A community 5K run will award $50 to the winner. 55 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.

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This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Probability and provides students with a clear perspective of the underlying concepts.

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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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