Question

Micki plays a game with Talia. There are 40 golf balls in a shoebox: 10 blue, 16 red, 4 green, 5 yellow, and 5 white. If Micki picks a blue, yellow, or white ball, she wins. If Talia picks a red or green ball, she wins. Is this game fair?

a) Yes, it's fair.
b) No, it's not fair.
c) The fairness depends on the prize.
d) The question doesn't provide enough information to determine fairness.

Answer 1

The probability of Micki winning is the same as the probability of Talia winning, both are 1/2. Since the chances of winning for both players are equal, the game is considered fair.

Step-by-step explanation:

To determine whether the game with the shoebox of golf balls is fair, we need to calculate the probability of winning for both Micki and Talia. Micki wins if she picks a blue, yellow, or white ball, and Talia wins if she picks a red or green ball. The total number of balls is 40 (10 blue + 16 red + 4 green + 5 yellow + 5 white).

The probability of Micki winning is the sum of probabilities of picking a blue, yellow, or white ball:

Adding these probabilities gives Micki a probability of winning: (10/40) + (5/40) + (5/40) = 20/40 or 1/2.

The probability of Talia winning is the sum of probabilities of picking a red or green ball:

Adding these probabilities gives Talia a probability of winning: (16/40) + (4/40) = 20/40 or 1/2.

Since both Micki and Talia have an equal chance of winning, with a probability of 1/2, this game can be considered fair. Thus, the correct answer to whether the game is fair is: a) Yes, it's fair.