Question

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?

○ 4
○ 6
○ 8
○ 10

Explanation:

Step1: Define fair game condition

A fair game has an expected value of 0. Let \(x\) = points for blue marble.

Step2: Calculate probabilities

Probability of blue: $\frac{1}{5}$; Probability of non-blue: $\frac{4}{5}$

Step3: Set up expected value equation

Expected value = (Blue value × Blue probability) + (Non-blue value × Non-blue probability)
$$0 = x \times \frac{1}{5} + (-2) \times \frac{4}{5}$$

Step4: Solve for \(x\)

Multiply both sides by 5: $0 = x - 8$, so \(x = 8\)

Answer:

8