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?

expected value (E) formula \[E = \int\limits_{}^{}x*P(x)\] translating this in simpler terms: to find the expected value, take the value of an event, multiply it by its probability. then repeat for all events. then sum up the results.

for a "fair" game the expected value should be 0 there is a 4/5 probability of drawing a losing marble and this event has the value of -2 points, since 2 points are lost for a losing marble likewise, there is a 1/5 probability of drawing the winning blue marble. we need to determine what point value it should have, so we'll call the value x for now using the formula: E = (4/5)(-2) + (1/5)x = 0 can you try solving for x?

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