The n-Children Problem

In 1959, Martin Gardner posed the Two-Children Problem and provided its solution. He later corrected his solution due to the ambiguity involved in the procedure of obtaining the given information. In 2010, Gary Foshee posed a generalization of Gardner’s problem by involving a second condition beyond gender, namely the birth-day of the week. This article generalizes the Two-Children Problem to n children with m conditions, and gives a formula to compute this probability under one explicit procedure of obtaining the given information.