As a project for math class, two students devised a game in which 3 black marbles and 2 red marbles are put into a bag.
First the players must decide who is playing black marbles and who is playing red marbles. Then each player takes a
turn at drawing a marble, noting the color, replacing the marble in the bag, and then drawing a second marble and noting
the color before returning it to the bag. The point scheme for the game is detailed in the table below.
Point Values for Marble Game
Black Marble Points
Red Marble Points
Both black: +2 points
Both red: +4 points
Different colors: -1 point
Different colors: -1 point
Both red: 0 points
Both black: 0 points
If Seth is challenged to a game by a classmate, which statement below is correct in all aspects in helping him make the
correct choice?
Since E(black) = 0.24 and E(red) = 0.16, Seth should choose to play black marbles.
E(red) will be twice that of E(black), so Seth should choose to play red marbles.
Since E(red) = E(black), it is a fair game, so it doesn't matter which color Seth chooses.
