Another chess problem by Jonathan Hsu

Any white square you choose, there are $\color{teal}{8}$ black squares that share the same row or column of the white square you chose. There are $\color{#EC7300}{32}$ black squares, so the probability is $\frac{\color{#D61F06}{8}}{\color{#20A900}{32}} = \color{#3D99F6}{0.25}$

For each white square you take, there are exactly 8 black squares that lie on the same row or column. There are 32 white squares, so there are $32*8 = 256$ ways to get a white and black square on the same row or column. There are in total $32*32 = 1024$ ways to choose a white and black square. So the probability is $\frac{256}{1024}$ = 0.25.