Let's say that when a child is born, the probability of it being a girl is 0.5.

Out of all the two-child families in the world, I have randomly selected one family that has a golden retriever named Waldo. One of the two children is a girl. What is the probability that the other one is a girl?

Solution

This is a fun problem to discuss as a class because some students will adamantly argue that the probability is 0.5. They'll say that the probability doesn't change just because you know the sex of the other child.

There are four possible ways that these two children could have arrived in the world: b-b, b-g, g-b, and g-g. The fact that you know that one is a girl eliminates the b-b families. In 2 out of 3 of the other families, the other child is a girl. So, the probability is 2/3 or 66.7%.

If you like this problem, then also take a look at the Monty Hall Problem.

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