A Boy Born on Tuesday
A family is chosen uniformly at random from all families with exactly two children in which at least one child is a boy born on a Tuesday. Each child is independently a boy or a girl with probability 1/2, and is born on each of the seven days of the week with probability 1/7, independently of sex. What is the probability that both children are boys? Give your answer as a reduced fraction.
Related problems & prerequisites
Worth solving first
- The Talkative Warden 5.0/10
- Monty Hall, Generalized 4.0/10
- Gold Coin in the Box 4.0/10
Source: Posed by Gary Foshee at the 2010 Gathering 4 Gardner; widely discussed since. Statement written for AxiomIQ.