In the land of Misogynia, parents only want to have boys.
If they have a boy, they stop having children.
If they have a girl, they keep trying to have a boy.
Out of 100 births, how many would be statistically likely to be girls? (We are assuming there is no technology to increase the chance of a boy or to abort a girl.)
The first new player to comment on the website with the correct answer wins a free drink at their next iQ Trivia show.
Fifty.
Even aside from all of that infinite series mumbo-jumbo, each birth is assumed to be a random draw with replacement. Collect any 100 births at random and the ratio should stay the same… all you’re doing is eliminating big brothers!
That’s exactly how it would work.
It’d be pretty impressive to keep procreating if there’s only boys…
We’re not saying it’s a likely scenario, but however you slice it, it would wind up being an even gender split.
I suspect this is a trick question.
If every birth is a new binary event (boy or girl) that is independent of any previous observation (have they had a boy yet or not), then there should be a 50:50 split per hundred.
I would have thought the only thing that would be skewed in the land of Misogynia would be the size of some broods. Half the families would have 1 child, a quarter would have 2 and so on.
Yes each birth is subject to random chance and you’d have an even split.
And, as you pointed out, some very odd family sizes.