King and Bishop

Discrete Mathematics Level 3

Dimitri places a Black King and a White Bishop on an empty chessboard. If the probability that Dimitri places the King and the Bishop on the chessboard such that the King is NOT in check (that is, the Bishop is not attacking the Black King), can be expressed as \(\dfrac{m}{n}\), in which \(m\) and \(n\) are coprime positive integers, find \(m+n\).

As an explicit example, if the Bishop is on \(f2\), the \(g1\), \(e1\), \(g3\), \(h4\), \(e3\), \(d4\), \(c5\), \(b6\) and \(a7\) squares are under attack.

Dimitri can place the Bishop either on a white or black square.

The King and the Bishop cannot be placed in the same square.

This is the third problem of the set Look after the King!

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