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This grid gives a visual way of calculating the answer to the question, “Among families that have two children, one of whom is a boy born on a Tuesday, how many have two boys?” It shows all the possible variations of birth day and gender for children in a two-child family. The families with the saturated colors are those which might qualify, while those that are shaded out are eliminated.

The row gives the birth day of the older child and the column gives the birth day of the younger, while the color represents the sex of each child. If the older child is a boy born on Tuesday, then the family must lie on the Tuesday row and the box representing the older child must be blue. If the younger child is a boy born on Tuesday, the family must lie on the Tuesday column and the box representing the younger child must be blue. The combination of all those boxes show all the possible families that qualify.

The total number of saturated boxes is 27. The number of saturated boxes in which both children are boys is 13. So the probability is 13/27. Credit: Bill Casselman