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