imc

When dividing each number on the wheel by $4,$ the remainders are $1,1,2,2,3,$ and $3.$ Each column on the checkerboard is equally likely to be chosen. When dividing each number on the wheel by $5,$ the remainders are $1,1,2,2,3,$ and $4.$ The probability that a shaded square in the $1$st or $3$rd row of the $1$st or $3$rd column is chosen is $$\frac{2}{3}\times \frac{3}{6}=\frac{1}{3}$$ The probability that a shaded square in the $2$nd or $4$th row of the $2$nd column is chosen is $$\frac{1}{3}\times \frac{3}{6}=\frac{1}{6}$$ Add those two together to get $$\frac{1}{3}+\frac{1}{6}=\frac{2}{6}+\frac{1}{6}=\frac{3}{6}=\boxed{\frac{1}{2}}$$