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7.4 The Mean

7.4 The Mean. It’s time for another Raffle!!!. Create a probability table depicting the situation and calculate the Expected Value two different ways. 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

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7.4 The Mean

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

  2. 7.4 The Mean Fair Bets Look back at the Raffle • 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? • 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?

  3. 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.”

  4. 7.4 The Mean Stocks 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? • 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

  5. 7.4 The Mean Stocks (again) 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? • 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

  6. 7.4 The Mean Life Insurance 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? • 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)

  7. 7.4 The Mean • Problems to complete for homework from section 7.4Pg. 365 #10 (silver dollar = $1, slug = $0), 11, 14, 15

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