Son whose name starts with 'M'
Discrete Mathematics
Level
4
Alice and Bob are chatting about their families.
Alice says, "I have two children."
Bob asks, "Do you have a son whose name starts with the letter 'M'?"
Alice replies, "Yes!"
Given that Alice was truthful, and assuming that a child's name will start with any given letter with probability 1/26 and that a child will be a boy with probability 1/2, what is the probability that Alice has two sons?
When your answer is in the form \(\frac{p}{q}\) for positive, coprime integers \(p\) and \(q\), input \(p+q\).
This is based off a well-known problem posed by Gary Foshee.
by
Maggie Miller