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Home > Student activities > National Maths Day > National Maths Day 2014 > A twist on Gardner's two children problem

A twist on Gardner's two children problem

Gardner's two children problem:

Mr Jones has two children. The older child is a girl. What is the probability that both children are girls?

Mr Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

The twist: Foshee’s two children problem:

Mr Ng has two children. One is a boy born on a Tuesday. What is the probability that both children are boys?

Surely knowing that one child was born on a Tuesday has nothing to do with it! Surprisingly enough, the additional information about the day of the week of the birthday does make a difference to the probability.

Read a detailed explanation in the Australian Mathematics Teacher journal Volume 70 Number 2 2014 entitled 'Gardner's two children problems and variations: Puzzles with conditional probability and sample spaces'.