Monday Math Problem #1: Expected Births

My colleague Max Lummis became a father over the weekend, so in order to wrap up the recent series of posts on expected value, here’s a birth-themed, three-part math problem for your Monday afternoon.

I’ll give a hat-tip to the person who introduced me to the problem after posting the solution in a few days. Feel free to reference Wolfram and the rules of expectations.

Suppose there’s parents that can have infinite children who really want a boy. They will have kids until they have a boy. The probability of any given child being a boy is 50 percent.

  1. What is the expected number of boys?
  2. What is the expected number of girls?
  3. What is the expected percentage of the children that will be girls?