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.

×

Problem Loading...

Note Loading...

Set Loading...