A newlywed couple are planning their family. They’d like to have four children, a mix of girls and boys. Which is more likely: (1) two girls and two boys or (2) three children of one sex and one of the other? (Assume that each birth has an equal chance of being a boy or a girl.)
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Most people guess that (1) is more likely, but in fact (2) is. There are 16 possible arrangements:
BBBB
GBBB
BGBB
BBGB
BBBG
GGBB
GBGB
GBBG
BGGB
BGBG
BBGG
GGGB
GGBG
GBGG
BGGG
GGGG
Eight of these have three children of one sex and one of the other; only six have two brothers and two sisters.
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