Marleny is creating a game of chance for her family. She has 5 different colored marbles in a bag: blue, red, yellow, white, and black. She decided that blue is the winning color. If a player chooses any other color, they lose 2 points. How many points should the blue marble be worth for the game to be fair?

For a fair game, the expected point change must be 0. The blue marble is chosen with probability 1/5 and is worth x points, while the other four marbles have probability 4/5 and each costs 2 points: (1/5)x + (4/5)(−2) = 0. Solving gives x = 8, so the blue marble should be worth 8 points.

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