Here’s a question for you:

John has two children. At least one of them is a boy.

What’s the probability that the other child is a girl?

Decide on an answer before moving on.







Intuitively, most people would guess that there’s a 50% chance that the other child is a girl.

If that’s your guess, keep reading, because that’s the wrong answer.

Answer: 66% Probability

Here’s how it works.

With two existing children, there are four possible scenarios:

  1. Boy & Boy (BB)
  2. Girl & Girl (GG)
  3. Boy & Girl (BG)
  4. Girl & Boy (GB)

Now since we know that John has at least one boy, we can eliminate the second scenario and have 3 possible outcomes:

  1. Boy & Boy (BB)
  2. Boy & Girl (BG)
  3. Girl & Boy (GB)

Among these 3 outcomes, 2 of them include a girl. So the answer is 2/3, or 66%.

Asking The Right Question

This answer might seem weird because although the question is:

Given two children with at least one of them being a boy, what’s the probability that the other child is a girl?

… you might have been thinking of this question instead:

What’s the probability of a parent having a baby girl?

The answer to the first question is 66%, while the answer to the second question is 50%.

This small example highlights the importance of understanding the question before looking for the answer.

Good Questions Are Hard To Find

People are often busy trying to find answers, but few question whether they truly understand the question they are asking.

Why is this important?

Because unless you understand the question, you wouldn’t recognize the right answer even if it were right in front of you.

Worse, you may think you have the right answer, when it is actually the right answer to a different question.