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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