
Almost absurd literary math puzzle - eruci
What is the probability that someone is an only son of an only son of an only son?
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AnimalMuppet
I'll start by assuming that the "someone" is male (if not, multiply the answer
by 1/2).

What's the probability that this person is himself an only son? I don't know
that it's logically derivable - couples have a variety of numbers of children,
of various mixes of genders. So far as I can see, that probability can be
measured but not derived. Call that probability P.

If I had to estimate it, I'd say that the most common number of children is
two, and of the four possibilities (BB, BG, GB, and GG), half of the boys are
only sons. (This is presuming that a sister doesn't ruin "only son" status.)
So that leaves the probability at 50%. Tweak that with only children (100% of
male only children are the only son) vs. more than 2 children (reduces the
probability of being an only son), but the probability is reasonably somewhere
in the neighborhood of 50%.

The probability we are looking for is P^3 (presuming that only-son-ness is not
something hereditable, that is, that the probabilities are independent in each
generation. So the total probability is something like 1/8 = 0.125 (or 1/16 if
we don't know that the "someone" is male).

Have I missed something here?

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yesenadam
That sounds right, as far as it goes. (I likewise assume a sister doesn't ruin
'only son' status, and that we don't know someone is male).

Another line of thought, possibly just a line of confusion:

Assume "someone", S, _is_ the OS of an OS of an OS. Look at the siblings of
S's grandfather - he could have had any number of sisters, but had no
brothers. The probability of that situation occurring goes down with each
increase in the number of sisters. So maybe an exact answer can be given, a
formula including terms for the number of sisters each of the 3 OSs have? (not
forgetting the probability that S is also female)

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eruci
Someone can be an only son regardless of the number of sisters he has

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yesenadam
>Someone can be an only son regardless of the number of sisters he has

Yes, that's what my point was - "he could have had any number of sisters" \-
if you have 12 sisters, it's extremely unlikely you are an only son. The more
sisters, the more unlikely being an only son is.

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eruci
Yep, but the whole trick is finding a model that estimates the percentage of
the male population that are 'only sons' at 0,1, and 2nd generation level.

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nicholas73
This is no more absurd than asking how many golf balls fit into a bus. It
seems impossible but with a few assumptions you can get a good enough
ballpark.

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eruci
That's why I wrote "Almost"

