Problem #123

A Game of Risk
Public 06/07/14 12xp Probability 51.7%

Two friends, Arya and Bran are being held captive in separate places. They request a trial by game from their captivators.

Here is the deal: Arya has to choose a random number between 1 and 101010101(inclusive). Bran has to choose also but between 1 and 303030303(inclusive). There is no possible communication between them and they will only be freed if the sum of their numbers is odd. Otherwise they are doomed forever.

What is the probability of them being freed? Give the answer as an irreducible fraction.

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Time may end, but hope will last forever.

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