Question

1. a jar has 10 red marbles, 6 purple marbles, and 4 turquoise marbles. grace wins if she selects a turquoise marble from the jar. is this game fair? why or why not?

yes, the game is fair because grace has equal probabilities of winning and losing.

no, the game is not 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.

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

Explanation:

Step1: Calculate total marbles

Total marbles = 10 (red) + 6 (purple) + 4 (turquoise) = 20.

Step2: Calculate winning probability

Probability of winning (turquoise) = $\frac{4}{20} = 0.2$.

Step3: Calculate losing probability

Probability of losing = 1 - 0.2 = 0.8 (or $\frac{16}{20}$).

Step4: Compare probabilities

Losing probability (0.8) > winning probability (0.2), so Grace is more likely to choose another color.

Answer:

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