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## Monday, November 9, 2015

### Marilyn Stirs the Pot...

 via WikiMediaCommons

We'll kickstart the week with an "Ask Marilyn" (Marilyn vos Savant) puzzle column, from yesterday's Parade Magazine. It's another of those easy-to-understand, but tricky, probability brainteasers:

A writer asks (and the wording is important), "Among parents with four children, what is the most common distribution of boys and girls? My friends think it’s two of each sex."
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Most would probably give the answer of 50/50, two boys and two girls. But Marilyn contends the most likely distribution is in fact three children of one sex and one of the other. She goes on to list ALL (16) of the possible birth outcomes:

(1) BBBB (2) BBBG (3) BBGB (4) BGBB (5) GBBB (6) BBGG (7) BGBG (8) GBBG (9) BGGB (10) GBGB (11) GGBB (12) GGGG (13) GGGB (14) GGBG (15) GBGG (16) BGGG

Then she notes that families with 3 children of one sex occur 8 different ways (or 50% of the time), while 2 of each sex occur in only 6 ways (or 37.5%).

She'll no doubt get pushback on this though (not uncommon for her) since the term "distribution," and the wording of the question, can be interpreted in crucially different ways:

Marilyn is only looking at distribution of "same" or "different" sexes, but if you look at distribution in terms of specific sexes then you have 2-boys/2-girls occurring in six cases, 3-boys/1-girl in four cases, and 3-girls/1-boy also in four cases... thus, the 50/50 boy/girl case IS indeed the most common.

Marilyn, you're such a troublemaker! ;-)