Problem:
A family has 2 boys and 3 girls. A newborn joins the family. Given that a randomly chosen child from the six children is a boy, what is the probability that the new child brought into the room is a boy?
Solution:
While the probability of a randomly chosen child is 1/2, you're given additional information that a randomly chosen child is a boy. Knowing this increases the chance that the newborn is a boy.
Let N be the sex of the new child, and R be the sex of the randomly chosen child. We want to compute P [N = b|R = b] . By Bayes’ Rule,
Notice the answer is not 1/2. Since we're using information we're given, we're able to say things with more certainty.
This is an absolute classic problem testing whether you know how to deal with dependency of random variables. Learn more about our services and how we can help prepare you for a career in Quant Finance!
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