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.