Question

probability models quiz
geometry b is (bva) 25-26 / probability

1. a jar contains 8 red marbles, 5 blue marbles and 3 green marbles. christopher wins if he picks a red marble and janet wins if he doesnt pick a red marble. is this game fair? why or why not?

yes, the game is fair because christopher and janet do not have an equal probability of winning.
no, the game is not fair because christopher has a higher probability of winning than janet.
no, the game is not fair because janet has a higher probability of winning than christopher.
yes, the game is fair because christopher and janet have an equal probability of winning.

Explanation:

Step1: Calculate total marbles

Total marbles = 8 (red) + 5 (blue) + 3 (green) = 16.

Step2: Probability Christopher wins

Probability (red) = $\frac{8}{16} = \frac{1}{2}$.

Step3: Probability Janet wins

Probability (not red) = $\frac{5 + 3}{16} = \frac{8}{16} = \frac{1}{2}$.

Step4: Compare probabilities

Both have probability $\frac{1}{2}$, so the game is fair.

Answer:

Yes, the game is fair because Christopher and Janet have an equal probability of winning.