Rooting For The Underdog Die

Probability Level 3

You and your friend are playing a dice game with the following rules:

  • You roll a fair 6-sided die, and your friend rolls a fair 8-sided die.
  • Whoever rolls higher wins the game.
  • If the rolls are the same, you will win the game.

If the probability that you win this game is ab\dfrac{a}{b}, where aa and bb are coprime positive integers, what is a+ba+b?


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