Common Core: S-MD.5
Problem 31 of 45s12-031
It costs $4 to play a game. You roll a fair die and are paid $15 for a 6, $6 for a 5, and nothing otherwise. Is the game fair? If not, who does it favour, and by how much per game?
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Solution walkthrough2:12
- A game is fair when the expected net gain is . Net gain is what you are paid minus the $4 to play.
- Net gains: a 6 gives , a 5 gives , and 1 to 4 give .
- Chances: a 6 is , a 5 is , and 1 to 4 is , since four of the six faces pay nothing.
- Weight each net gain by its chance and add: .
- The long-run average is per game, below : not fair, and it favours the house.
- Traps: $3.50 forgets the cost, $3 is a plain average of the prizes, and $1.83 drops the losing rolls.