13
Part of 2006 AMC 10
Problems(2)
Shooting dice
Source: AMC 10 2006A, Problem 13
2/6/2006
A player pays to play a game. A die is rolled. If the number on the die is odd, the game is lost. If the number on the die is even, the die is rolled again. In this case the player wins if the second number matches the first and loses otherwise. How much should the player win if the game is fair? (In a fair game the probability of winning times the amount won is what the player should pay.)
probabilityAMC
Coffee and Cream
Source: AMC 12 2006B, Problem 11
2/17/2006
Joe and JoAnn each bought 12 ounces of coffee in a 16-ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee?
ratioAMC