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The Birthday Paradox Explained
Is it even a paradox?
We humans are not the best at understanding probability. A classic example of this is the Monty Hall Problem: a brain teaser based on an older game show. This seemingly simple probability puzzle has a very counterintuitive result. While the Monty Hall Problem gets the most attention, there are plenty of other examples of how our probability intuition fails us.
Another classic probability brain teaser is called the Boy or Girl Paradox, sometimes called the Two Child Problem. Consider the following two questions.
- 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 girl. What is the probability that both children are girls?
Take a moment to think this through before seeing the solution below.
People commonly assume that both questions are equivalent and that each has a 50% chance of being correct. That is not the case! Our probabilistic intuition leads us astray here. We can easily solve these problems by considering all possible outcomes. For the sake of this problem, we will assume that the probability of having a boy or a girl is 50% for the first and second child.
