State Math Contest

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Current Exams

2008 Exams:
  • 7-9 Junior Exam
  • 10-12 Senior Exam
  • 7-9 Junior Exam Solutions
  • 10-12 Senior Exam Solutions

    Note: After the exam, it was brought to my attention that there is an ill-defined problem on both the Junior and Senior exams. It is the problem about having 50 coins that add to a dollar and one of the coins is dropped. The question asked what is the probability that the dropped coin is a penny. (It is question #20 on the Junior exam and #16 on the Senior exam.) If you check the solutions posted here, you'll see that I calculated the answer based on the assumptions that (1) dropping any coin is equally likely whether it's a penny, nickel, dime or quarter, and (2) each of the two coin distributions that fit the given conditions is also equally likely. Since we did not explicitly state the equal likelihood of these things in the question, the actual correct answer is (e) "There is not enough information." Answer (c) "85%" is the advertised correct answer, based on the equal likelihood assumptions.

    I have conferred with several colleagues about what seems most fair in this situation. I have also checked with the person who will be scanning/grading the answer bubble sheets so I know all of our options on that end. After gathering all of this necessary input, I have decided to accept both answers (e) and (c) as correct for this problem. If you have further questions, you may email me, Kelly MacArthur, at

Department of Mathematics       College of Science       University of Utah