WASHINGTON STATE MATHEMATICS COUNCIL

2000 MIDDLE SCHOOL MATH OLYMPIAD

 

 

Session I

SEVENTH GRADE PROBLEM SOLVING

7

 

The Tiles Game

Lindsay has three bags with tiles in them. Each bag has six tiles which are numbered 1, 2, 3, 4, 5, and 6, as shown below. Lindsay reaches into each bag and randomly draws out one tile. 

 

Lindsay adds up the two largest numbers. So, for instance, if she drew tiles that were 4, 3, and 2, she would add up the 4 and 3 to get 7. If she drew tiles that were 4, 2, and 2, she would add up the 4 and 2 to get 6. 

 


The problem is to figure out what the probability is of getting a 7 in this kind of game, in which you add the top two of three tiles drawn. 

 


Show us your work. The people who read your paper are looking at: