# SOLUTION: How would you put this in expected value and fair price of ticket? 1000 tickets for prizes are sold for \$2 each. Seven prizes will be awarded – one for \$400, one for \$200, and f

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 Question 150573This question is from textbook a survey of mathematic with applications : How would you put this in expected value and fair price of ticket? 1000 tickets for prizes are sold for \$2 each. Seven prizes will be awarded – one for \$400, one for \$200, and five for \$50. Steven purchases one of the tickets. (Give solutions as decimals accurate to the nearest hundredth.) a) Find the expected value b) Find the fair price of the ticket. This question is from textbook a survey of mathematic with applications Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!How would you put this in expected value and fair price of ticket? 1000 tickets for prizes are sold for \$2 each. Seven prizes will be awarded – one for \$400, one for \$200, and five for \$50. Steven purchases one of the tickets. (Give solutions as decimals accurate to the nearest hundredth.) a) Find the expected value ``` Note that we include -\$2 as a "negative prize" in the likelihood that Steven doesn't win at all and loses his \$2. Prizes | Probability | Expectation \$398 | .001 | \$0.398 \$198 | .001 | \$0.198 \$ 48 | .001 | \$0.048 \$ 48 | .001 | \$0.048 \$ 48 | .001 | \$0.048 \$ 48 | .001 | \$0.048 \$ 48 | .001 | \$0.048 \$ -2 | .993 | -\$1.986 ------------------------------------- Total expectation = -\$1.15 The expected value is -\$1.15 or a LOSS of \$1.15 That is, if this raffle were held every week, and Steven played it every time, he would average losing \$1.15 per game. --------------------------------------------------------- b) Find the fair price of the ticket The easiest way to do this problem is just to pretend that they give him his ticket price back in the problem above. So we then just add \$2 to the -\$1.15 and get \$2 - \$1.15 = \$0.85. But to work it out: Let the fair price be \$x We put -x where we put -2 above and -.993x for the expectation, and 0 for the Total expectation: Prizes | Probability | Expectation \$400-x | .001 | \$0.40-.001x \$200-x | .001 | \$0.20-.001x \$ 50-x | .001 | \$0.05-.001x \$ 50-x | .001 | \$0.05-.001x \$ 50-x | .001 | \$0.05-.001x \$ 50-x | .001 | \$0.05-.001x \$ 50-x | .001 | \$0.05-.001x \$ -x | .993 | -\$0.993x ------------------------------------- Total expectation = \$0.000 Add the right column and make an equation: 0.85 - x = 0 0.85 = x That is, if this raffle were held every week, and the price were 85 cents, and Steven played it every time, he would average breaking even. That fair ticket price is 85 cents. Edwin```