Sample Questions

1. One scratch ticket game has the probability distribution shown to the right.
   1. Find and explain the meaning of the expected value for this scratch ticket game
   2. What would be a fair price for this ticket game?
      
      
2. At a local carnival people can pay $5 to spin a spinner like shown below.
   
   Although the players pay $5 per spin, they can win $10 if the spinner lands on purple. They don't win anything if the spinner lands on yellow. How much should they win when the spinner lands on red so that the game is fair?
   
   

Sample Response

1. The expected value for this ticket game is $1*(4/10) + $2*(2/10) + $3*(2/10) + $5*(1/10) + $0*(1/10) = $1.90.
   That means that a player should expect to average to win $1.90 for every scratch ticket provided that the player plays a LOT of games. A player won't win $1.90 for a single game, but on average a player would win $1.90. For example, if a player played 1,000,000 scratch tickets then he or she should expect to win $1,900,000 which averages to $1.90 per game.
   Also, $1.90 would be the "fair price" to charge for the game.
   
   
   
2. P(yellow) = 1/2. P(purple) = 2/12. P(red) = 4/12.
   
   
   

   Color	Prize Value ($)	Probability
   Yellow	0	1/2
   Purple	10	2/12
   Red	x	4/12

   
   
   Expected value of one spin should be $5
   5 = 0*(1/2) + 10*(2/12) + x*(4/12)
   5 = 20/12 + x/12
   60 = 20 + x
   x = 40.
   
   To be a fair game, they game should pay $40 for landing on red.
   Double check: $0*(1/2) + $10*(2/12) + $40*(4/12) = $20/12 + $40/12 = $60/12 = $5.