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WASHINGTON STATE MATHEMATICS COUNCIL 2000 MIDDLE SCHOOL MATH OLYMPIAD Session I EIGHTH GRADE PROBLEM SOLVING

8

The Tiles Game

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

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:

• YOUR ANSWER
• YOUR UNDERSTANDING OF THE PROBLEM
  Do you understand what the problem is asking? What did you notice about patterns?How did that help you solve the problem?
• HOW YOU COMMUNICATE:
  Is your reasoning about the problem and about your strategies clearly communicated -- using words, pictures, tables, symbols?
• YOUR REASONABLENESS CHECK:
  How did you check that your answer was reasonable?