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Two Children, One Is a Boy: What's the Chance Both Are Boys?
A family has two children. We know that at least one of them is a boy. What is the probability that both children are boys? (Assume equal probability for each gender.)
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What is the answer to the two children probability riddle?
The probability that both children are boys is 1/3. Knowing at least one is a boy leaves three equally likely cases (BG, GB, BB), and only one of them is BB.
Why isn't the answer 1/2?
Because the condition 'at least one boy' rules out only the girl-girl case, leaving three outcomes, not two. Only one of those three is two boys, so the answer is 1/3, not 1/2.
What is the boy or girl paradox?
It's a famous probability puzzle showing that knowing one child is a boy changes the odds the other is a boy from 1/2 to 1/3, depending on how the information is given.