Problem:
In a particular game, each of players rolls a standard -sided die. The winner is the player who rolls the highest number. If there is a tie for the highest roll, those involved in the tie will roll again and this process will continue until one player wins. Hugo is one of the players in this game. What is the probability that Hugo's first roll was a , given that he won the game?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since we know that Hugo wins, we know that he rolled the highest number in the first round. The probability that his first roll is a is just the probability that the highest roll in the first round is .
Let indicate the probability that event occurs. We find that (No one rolls a 6No one rolls a 5 or 6 (The highest roll is a ),
So,
The problems on this page are the property of the MAA's American Mathematics Competitions