An unintuitive probability question Suppose you meet a stranger in the Street walking with a boy. He tells you that the boy is his son, and that he has another child. Assuming equal probability for boy and girl, and equal probability for Monty to walk with either child, what is the probability that the second child is a male?
The way I see it, we get to know that the stranger has 2 children, meaning each of these choices are of equal probability:
(M,M)
(M,F)
(F,M)
(F,F)
And we are given the additional information that one of his children is a boy, thus removing option 4 (F,F). Which means that the probability of the other child to be a boy is 1/3. Am I correct?

I believe you're correct, the answer 1/3 is correct based on the wording of your problem. According to your problem, there is no specification on whether the boy is the oldest or youngest and therefore, the boy's siblings can either be a older sister, younger sister, or a brother. Notice that the boy can't have an older or younger brother, because the probability of having an older sister would then be twice as large as having an older brother.
It also seems like in this problem, according to the wording, you're CHOOSING, beforehand all the two children families, and then EXCLUDING all the girl-girl families, leaving you with at least one child being a boy.
You're not choosing a boy, and then saying that he is part of a two-sibling family. If that were the case, it would be the same question as asking: What is the probability that the boy's to-be-born sibling will be a boy? The answer is obviously 1/2, because it's either a boy or girl.
However, in your problem you are CHOOSING a boy, because there is no specification, and therefore, the ordering of the siblings can be in any ordering, leaving u with twice the probability of having a sister rather than a brother.
