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Boy or Girl Paradox
All statistics tools
A famous probability puzzle about conditional probability.
Scenario
Mr. Smith has two children.
Given Information:
1. At least one of them is a Girl
We know not (Boy, Boy).
2. The OLDER child is a Girl
We know first child is Girl.
Explanation
Probability (Both are Girls)
1/3
Sample Space Analysis
Older
Younger
Valid?
Result
Boy
Boy
No
Excluded
Boy
Girl
Yes
GG? No
Girl
Boy
Yes
GG? No
Girl
Girl
Yes
GG!
Count the "Yes" rows. Calculate (GG Rows) / (Yes Rows).
About this calculator
Overview
The Boy or Girl paradox asks about the probability of a family having two girls (or boys) given specific information about one of the children.
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Pro Tips
Think about the Sample Space of all possible families: BB, BG, GB, GG.
!
Fun Facts
"The answer changes depending on exactly how the information is obtained."
"In reality, boy births are slightly more common than girl births (approx 1.05:1)."
