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Problem of the Day #142: A Guessing Game August 8, 2011

Posted by Saketh in : potd , trackback

Albert and Billy are playing a guessing game. They begin by filling a jar with $10$ white marbles and $10$ black marbles. Albert then draws out all $20$ marbles one by one, asking Billy each time to guess the color that will be drawn next.

Albert will give Billy a dollar for each correct guess. Billy, being a highly skilled marble guesser, plays optimally. Suppose he can expect to win $\$\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute the value of $a+b$.

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