Coding Horror: Finishing The Game
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Coding Horror: Finishing The Game
1–10 of 41 posts
Re: Coding Horror: Finishing The Game
#2URGH! I just lost :(
Re: Coding Horror: Finishing The Game
#3Sorry Jeff, I understand the problem, but the language of the setup was wrong. Since a PERSON told you they have one girl, the GB and BG are equivalent and collapse to one case instead of two in the way that normal people talk.
If you had said that a mathematician or a statistician said they have one girl, that would be a different story.
Re: Coding Horror: Finishing The Game
#4This kind of problem comes up all the time in a poker tournament. Each person has a different number of chips in front of them, and when they reach the final table, since so much money is at stake, they want to make a deal. How do you determine a fair deal when each person has a different number of chips and prizes are radically different for first, second, and third place. Fun problem. Answer: The independent chip model
Gambling to the rescue
Re: Coding Horror: Finishing The Game
#5Interesting theory, I'd never thought of every possibility, especially in this context, where we are talking about a person, I was thinking about human psychology or behavior when I first read that article.
Re: Coding Horror: Finishing The Game
#6Sorry Jeff, I understand the problem, but the language of the setup was wrong. Since a PERSON told you they have one girl, the GB and BG are equivalent and collapse to one case instead of two in the way that normal people talk . If you had said that a mathematician or a statistician said they have one girl, that would be a different story.
I'm not sure what you mean be equivalent, but the relevant point is that a family is twice as likely to have one boy and one girl than have two girls.
Re: Coding Horror: Finishing The Game
#7This kind of problem comes up all the time in a poker tournament. Each person has a different number of chips in front of them, and when they reach the final table, since so much money is at stake, they want to make a deal. How do you determine a fair deal when each person has a different number of chips and prizes are radically different for first, second, and third place. Fun problem. Answer: The independent chip m…
It is very clearly mirrored in backgammon theory, where touneament players memorize "match equity" tables and use them to govern their use of the doubling cube.
Re: Coding Horror: Finishing The Game
#8Jeff didn't phrase the question carefully enough. In English if you say, "I have two children, one is a girl" that CANNOT mean both are girls. If both were girls you would never say that. Saying you have 1 girl implies that you have 1 boy. Or maybe 1 girl and one hermaphrodite.
100% was the right answer.
It's easy to get people to argue when you give them an almost-ambiguous word problem; they're not arguing about the math, they're arguing about the mapping from ambiguous words to math.
Re: Coding Horror: Finishing The Game
#9Sorry Jeff, I understand the problem, but the language of the setup was wrong. Since a PERSON told you they have one girl, the GB and BG are equivalent and collapse to one case instead of two in the way that normal people talk . If you had said that a mathematician or a statistician said they have one girl, that would be a different story.
I don't think you do understand the problem. The thing you're taking issue with - GB vs BG - is the vitally important to the statistics, and is the thing that "normal" people get wrong when they see this kind of problem for the first time.
The only real objection to the problem as it's posed is that it's pretty unlikely that anyone would say that one of their children was a girl when both of their children are girls. For a normal conversation, the ambiguity wouldn't be present; "two children" combined with "one is a girl" means the chances of one boy and one girl are 100%.
It's a bit like the old joke about "which month of the year has 28 days?" - answer being, they all have 28 days, just some have more.
However, in other less contrived situations, this is important. People risk discounting permutations, and only considering combinations, when the permutations are necessary to get a correct view of the odds.
Re: Coding Horror: Finishing The Game
#10Saying "A person has two children, at least one of which is a girl. What is the probability that both of the children are girls?" would more clearly explain the problem.