My Math Forum Probability question with dice

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 March 15th, 2011, 03:48 AM #1 Newbie   Joined: Mar 2011 Posts: 2 Thanks: 0 Probability question with dice Dear all I have a problem which seems very easy, but I still can't wrap my head around the math of it. If I roll a large series of 6-sided dice, the average should be ca. 3.5. So far, so good. However, if I were allowed to always roll two dice, and pick the highest for each cast, what would be the new average? Surely, this isn't the same as rolling a certain amount of dice and simply crop the higher half of the results -- or is it? I may be confusing myself with the procedure. Looking forward to your help!
 March 15th, 2011, 04:23 AM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Probability question with dice Throwing two dice and taking the maximum: $\begin{array}{c|cccccc}&1&2&3&4&5&6\\\hline\\ 1&1&2&3&4&5&6\\ 2&2&2&3&4&5&6\\ 3&3&3&3&4&5&6\\ 4&4&4&4&4&5&6\\ 5&5&5&5&5&5&6\\ 6&6&6&6&6&6&6 \end{array}$ Each entry in the table has the same probability, so sum them and take the average. The array is symmetrical. Twice the upper-right triangle + the leading diagonal = 2 (1.2 + 2.3 + 3.4 + 4.5 + 5.6) + (1+2+3+4+5+6) = 161 161 / 36 = 4.47222...
 March 15th, 2011, 04:55 AM #3 Newbie   Joined: Mar 2011 Posts: 2 Thanks: 0 Re: Probability question with dice Thanks, aswoods, it's quite clear now

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