## Roll of the Dice

Another puzzle from the NY Times Number Play:

Wouter throws three dice.These dice look just like ordinary dice, but their faces are numbered differently.The first die has the numbers 1, 1, 2, 2, 3 and 3 on it.The second die has the numbers 2, 2, 4, 4, 6 and 6 on it.And the third die has the numbers 1, 1, 3, 3, 5 and 5 on it.He then adds up the numbers he gets from rolling the three dice.What is the probability that the resulting number is odd?

I will have the naive assumption of uniform distribution of outcomes. The second die faces are all even and the third die all odd, hence their sum is always odd. Therefore, the probability the sum of the faces of the three dice is odd=probability die 1 is even =1/3.

Simulation of 10 one thousand throws of the dice are reassuring.

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