# Math (Probability)

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Bret and Shawn are playing a game where each turn the players roll a 20-sided die fair and then add the number they get to their score. The winner is the player with the highest score at the end of the game (there may be a tie). Before the last turn, Shawn is winning by 10 points. The probability that Bret can come back and win the game can be expressed as ab where a and b are coprime numbers. What is a+b?

• Math (Probability) -

The size of the sample space of the last throw is 20*20=400.
Out of the 400 outcomes, Bret needs those where his throw is 11 or more than Shawn's, namely:
(12,1),(13,1),(14,1)...(20,1)
(13,2),(14,2)...(20,2)
...
(19,8),(20,8)
(20,9)

There are ∑(i), i=1,9 outcomes.
Can you figure out the probability, and a+b?

• Math (Probability) -

Please tell the answer. I'm not able to get it.

Thanks.

• Math (Probability) -

89

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