Fair’s Fair ?

 When you throw a pair of ordinary six-sided dice, and add their scores together you can get a total ranging from 2 to 12.

These scores occur with probabilities shown by the ‘possibility space’ diagram below.

 For example, a score of 10 can occur in three different ways out of the thirty-six  ways possible, indicating a probability of 

   

The Problem:

One of the dice is adapted slightly by changing the 2 to an 8.

Can you adapt the second dice so that they still perform in exactly the same way when thrown as a pair? It does seem extremely unlikely, but strange things are possible in Mathematics !

i.e. the probability of a total of 10 remains   , as before, and similarly for all the other totals from 2 to 12.

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Last modified: June 18, 2007