A problem by Josh Rowley

Level pending

Xavier has 1000 coins and Yvonne has 999 coins. Let x denote the number of tails face up on Xavier's coins and y denote the number of tails face up on Yvonne's coins. The probability that \( y\ge x \) can be expressed as a/b where a and b are positive coprime integers. What is a + b?

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