Wednesday, January 18, 2012

Is the Answer Obvious, or, Obscure

 Verbatim from Richard Wiseman's blog:
"Imagine there is a country with a lot of people. These people do not die, the people consists of monogamous families only, and there is no limit to the maximum amount of children each family can have. With every birth there is a 50% chance its a boy and a 50% chance it is a girl.  Every family wants to have one son: they get children until they give birth to a son, then they stop having children. This means that every family eventually has one father, one mother, one son and a variable number of daughters.  What percent of the children in that country are male?"
Wiseman's Friday puzzles are frequently devious… but, often once the answer is given and explained, one feels impelled to slap one's forehead and exclaim "DOH!, well, of course!." So perhaps his best offerings are those that, even once explained, are still not totally clear, and generate a lot of ongoing discussion/debate...

The one from last Friday (above) is such an effort, once again proving how tricky and misleading, probabilities can be. I confess to requiring extra time to convince myself that 50% was the correct answer, and it stiiiill rankles my intuition (…reminds me of Cantor's "I see it but I don't believe it" reaction! ;-)). This seems to be one of those quirky puzzles that is patently obvious to many, yet hugely thorny for others (one of the keys, I think, is to remain tightly focused on strict statistical probability, and not let your brain get distracted by what could theoretically happen). Read all the discord for yourself:

(...peruse as many of the 270+ comments as you care to -- in fact you have to read some to get the answer, since Richard neglected to post an answer or explanation in his own post).

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