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7.4 The Mean Its time for another Raffle!!! Another local charity is holding a raffle. They are selling 1,000 tickets for $25 each. 1 st Prize: $5,000 2 nd Prize: $1,000 3 rd Prize: $500 Is it worth it for you to buy a ticket? Create a probability table depicting the situation and calculate the Expected Value two different ways. ValueProbability ValueProbability

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7.4 The Mean Fair Bets Casinos, Carnivals, State Fairs all have one goal in mind: MONEY! Each of these entities will have game with a negative expected value. If E(x) = 0, it is considered the break-even price. – What is break even? Look back at the Raffle ValueProbability We need to consider the ticket price in the value now The only question remaining: what do we charge per ticket to make this a break-even value?

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7.4 The Mean In order to calculate this, we need to remember the break- even point is when E(x) = 0 Therefore, calculate the expected value and set it equal to 0. 0 = (20000 – z)(0.0001) + (500 – z)(0.002) + (0 – z)(0.9979) 0 = 2 – 0.0001z + 1 – 0.002z + 0 – 0.9979z 0 = 3 – 1z 3 = z Therefore, each ticket should be $3 in order to make this worth your while. ValueProbability 20000 – z0.0001 500 – z0.002 0 – z0.9979

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7.4 The Mean Stocks Suppose it is known that by the start of next week the stocks for ABC company will be worth: $40 per share with a 15% probability $20 per share with a 25% probability $0 per share with a 60% probability Create a probability table using a random value for the price of the stock. Calculate the fair (break- even) price for this stock. What does this mean in the context of the problem? PriceProbability

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7.4 The Mean Stocks (again) Suppose you are still looking to buy stock in the ABC company, yet the following new information was obtained: $40 per share with a 20% probability $20 per share with a 30% probability $0 per share with a 50% probability Create a probability table using a random value for the price of the stock. Calculate the fair (break- even) price for this stock. Does your choice to buy/not buy this stock change? PriceProbability

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7.4 The Mean Life Insurance According to life insurance tables, The probability of a 74 year old man will live an additional five years is 0.7. How much should a 74 year old man be willing to pay for a policy that pays $2000 in the event of death at any time within the next 5 years? (Do not take interest rates and inflation into consideration) Create a probability table using a random value for the price of the insurance. Calculate the fair (break- even) price for the insurance. Should you buy the insurance? PriceProbability

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7.4 The Mean Problems to complete for homework from section 7.4 Pg. 365#10 (silver dollar = $1, slug = $0), 11, 14, 15

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Copyright © Cengage Learning. All rights reserved. CHAPTER 9 COUNTING AND PROBABILITY.

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