Re: Kiddie question


With no time limit, yes. (Each couple has more daughters than sons
eventually.)

I beg to differ...

How can you combine equal probabilities of an event to get an unequal
probability?

With no time limit, "eventually" can be as large as you like (or
need)...

A population with infinite lifetimes and infinite breeding lifetime
that followed the protocol under discussion ( have kids until
girls>boys) would always have a statistically equal number of boys and
girls. The number of families that have g>b and quit would always be
balanced by the families that are behind (possibly <way> behind) and
still trying...

We start with a certain finite number of couples. Any given couple,
according to the laws of probability, will eventually reach a state
of more girls than boys. Because there are only finitely many
couples, ALL of them reach that state at some time. It is a random
time, but (almost surely) finite. In the total of all randomly
possible universes, there are always an equal number of boys and girls.
But in any fixed universe, eventually we reach the ending state with
more girls than boys.


This is like the strategy for winning at a casino: if you're ahead
stop; otherwise bet enough to cover your losses and make a bit more.
It works if you have an unlimited supply of money, but in that case
why would you be gambling?

Again, there would be enough people with an infinite amount of money
trying to get back to even, to match all the players who get ahead and
quit. The casino would have their money in the meantime.

Reality check: Unlike the situation with card counting in Blackjack,
no one ever got banned from a casino for playing your strategy, and
the casinos never claimed that someone had too much money to play the
casino's games...


--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.

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