# Random Colourings of a Chessboard

The squares of a $$3 \times 3$$ board are randomly coloured black or white. Let $$W$$ be the number of white squares and $$B$$ the number of black squares. The expected value of $$\vert B - W \vert$$ can be expressed as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a + b$$?

Details and assumptions

The board is blank at the start.

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