CCSS Honors 2.4 Example 2

Sylvia and her brother Nate make a deal. Each sibling will play a game of chance 100 times and the player who wins the most points has to do the dishes for a week. Sylvia chooses to spin for her points, while Nate chooses to roll a 12-sided die. Sylvia’s spinner has 10 equally sized, numbered sections. If the spinner lands on 3 or 7, she wins 50 points. Otherwise she wins nothing. Nate rolls a 12-sided number die. Prior to rolling the die, he chooses a number between 1 and 12. If he rolls that number, he wins 100 points. Otherwise he wins nothing. Who do you predict will have to wash dishes for a week? Determine the expected value for each player’s chance of winning, and use it to explain your choice.
  1. Find the expected value for Sylvia’s game.
  2. Find the expected value for Nate’s game.
  3. Compare the expected values and draw conclusions.