why the odds of the “two children problem” are 1/3?

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I was asked the question “a man states he has two children, and at least one of them are boys, what are the odds that the man has two boys?” I’ve been told the answer is 1/3, but I can’t wrap my head around it. Additionally, there is another version of the problem that states he has at least one boy born on a Tuesday. How does that change the odds? Why?

Edited to add (so people don’t have to sort through replies): the answer is 1/3 because “at least one boy” is accounting for B/G & G/B. The girl can be the first or second child. You can move the odds to 50/50 by rewording the question to “my first of two children is a boy, what are the odds the other child is a boy”

In: Mathematics

27 Answers

Anonymous 0 Comments

This question has many variants but to solve this version.

If you have a family with 2 children and at least 1 is a boy but gave no more information then the only possible outcomes for the family can be BB GB BG. That is 1 in 3.

If you cant wrap your head around it,

Imagine walking into a room with 2 silhouettes and you were told one of these is a boy what are the chances both are boys? As you don’t know which one is the boy but one has to be a boy then your options can only be BB GB BG. 1 in 3.

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