Rooks on a board

Probability Level 2

What is the probability that a white rook and a black rook placed on a chess board won't threaten each other?

\frac{48}{63}

\frac{47}{63}

\frac{49}{63}

\frac{50}{63}

1 solution

Caleb Townsend
Apr 9, 2015

Assuming they are placed uniformly, randomly, and without stacking, and that there are no other pieces:

After the first rook is placed, it attacks $14$ squares total, independent of placement. The second rook can be placed in $63$ squares, only $63-14=49$ of which are safe. The fraction of safe spaces is $\frac{49}{63} = \frac{7}{9}$

Rooks on a board

1 solution

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