What is the probability that this child has a brother?
Puzzle solution:
The correct answer is: 1/3.
The intuitive answer of 1/2, based on the argument that the births of the two children are independent of each other, is incorrect because the problem does not reveal which of the two births is a son. In fact, there are four possibilities for how the genders of the children can be distributed: BB, BG, GB and GG, of which only one, GG, is eliminated, since we know that at least one of the children is a boy. That leaves the three possibilities BB, BG and GB, each of which is equally likely. GG therefore has a probability of 1/3.
Did you enjoy this probability puzzle? Did you understand the solution? Feel free to leave a comment..