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415 probability/oldest.girl.p




Description

This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

415 probability/oldest.girl.p


You meet a stranger on the street, and ask how many children he has. He
truthfully says two. You ask "Is the older one a girl?" He truthfully
says yes. What is the probability that both children are girls? What
would the probability be if your second question had been "Is at least
one of them a girl?", with the other conditions unchanged?

probability/oldest.girl.s

There are four possibilities:

    Oldest child    Youngest child
1.  Girl            Girl
2.  Girl            Boy
3.  Boy             Girl
4.  Boy             Boy

If your friend says "My oldest child is a girl," he has eliminated cases
3 and 4, and in the remaining cases both are girls 1/2 of the time. If
your friend says "At least one of my children is a girl," he has
eliminated case 4 only, and in the remaining cases both are girls 1/3
of the time.

 

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