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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