Question

Suppose there is a game of chance that you would like to play. It costs $3 to play one time. There are 100 $1 bills, 20 $5 bills, 3 $20 bills, and 1 $100 bill in a box. You may reach into a box without looking and select one bill. Is this a fair game? Why or why not?

Answer 1

1. It is not a fair game.

2. The game is not fair because the probability of winning and the probability of losing are not equal. In a fair game, the probability of winning is equal to the probability of losing. In this game, the probability of losing is 0.81 or 81%, while the probability of winning is 19% (100 - 81).

Explanation:

Cost of playing the game one time = $3

Total number of bills in the box = 124 (100+20+3+1)

Chance of losing is represented by 100 of $1 bills = 100/124 = 0.81 or 81%

Chances of losing are represented by 20 of $5 bills, 3 of $20 bills, and 1 $100 bill = 0.19 or 19% (20/124 + 3/124 + 1/124).