Probability That Both Children Are Boys

Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?


The probability is 1/3.

There are initially 4 possibilities: girl-girl, girl-boy, boy-girl and boy-boy. Since at least one of them is a boy (but we don’t know if it’s the first or second child), we can rule out the girl-girl combination.

Only one out of the 3 combinations is boy-boy, so we get a probability of 1/3.

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