# 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.

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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

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?

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

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

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

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

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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