Question

A jar is filled with 60 different colored marbles, 12 of which are red, 23 of which are blue, and 25 of which are green. A player is asked to draw a single marble from the jar and if they draw a red marble they will win $20, if they draw a blue marble they will lose $10, and if they draw a green marble they will lose $5. You may round your answer to the nearest cent.

What is the expected outcome of this game?


Would it be profitable over time to play?

Answer 1

Explanation:

To find the expected outcome, we need to calculate the probability of drawing each color marble and then multiply it by the corresponding dollar amount:

Probability of drawing a red marble = 12/60 = 1/5

Probability of drawing a blue marble = 23/60

Probability of drawing a green marble = 25/60 = 5/12

Expected outcome = (1/5)*$20 + (23/60)*(-$10) + (5/12)*(-$5) ≈ -$1.08

Therefore, on average, a player can expect to lose about $1.08 per game.

Playing this game over time would not be profitable as the expected outcome is negative.