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February PoTM

Jeffrey rolls three fair six-sided dice. What is the probability that the mean of the three results is equal to the median of the three results? Express the probability as m/n in lowest terms and compute m + n.

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Written by Chelsea Lu

 

Submit your answers in the Google Form: https://docs.google.com/forms/d/e/1FAIpQLScmHCygd3srEH7s6VkcmLDFbKDvMiG9wfATU0-mR74AuM1Flw/viewform

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Stuck? Check out these resources and hints:

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  1. Let the three rolls be rearranged in nondecreasing order: a < b < c. Then the median is b. Translate “mean equals median” into the equation (a+b+c)/3 = b.

  2. Interpret the condition the problem gives: it forces a, b, c to be in arithmetic progression (equally spaced). Now count how many suchtriples can happen with values 1 through 6, and remember to convert from sorted triples to ordered dice outcomes.

 

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