A jar has 10 red marbles, 6 purple marbles, and 4 turquoise marbles. Grace wins if she selects at turquoise marble from the jar. Is this game fair? Why or why not?

Question

Yes, the game is fair because Grace has equal probabilities of choosing a marble of either color.

Yes, the game is fair because Grace has equal probabilities of winning and losing.

No, the game is not fair because Grace has a higher probability of choosing a marble of another color.

No, the game is not fair because Grace has equal probabilities of winning and losing

Answer 1

A fair game is defined as any game where the expected average payout would be equal to 0. If a win = 1, and a loss = -1, we could set up a relationship multiplying these payouts by their probabilities.

1(4/20) + -1(16/20) = ?

If this were a fair game, this relationship should equal 0. However, you notice that the actual value ends up being -12/20 or -3/5. This shows that she has an average payout much lower than 0.

No, the game is not fair because Grace has a higher probability of choosing a marble of another color.