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Comment author: Alicorn 06 May 2011 06:30:09PM 0 points [-]
Comment author: matteri 06 May 2011 06:43:23PM 0 points [-]

Very well, I could have phrased it in a better way. Let me try again; and let's hope I am not mistaken.

Considering that even if there is such a thing as an objective probability, it can be shown that such information is impossible to acquire (impossible to falsify); how could it be anything but religion to believe in such a thing?

Comment author: Alicorn 06 May 2011 06:18:52PM 3 points [-]

It is not necessary to know the exact bias to enact the following reasoning:

"Coins can be rigged to display one face more than the other. If this coin is rigged in this way, then the face I have seen is more likely than the other to be the favored side. If the coin is not rigged in this way, it is probably fair, in which case the side I saw last time is equally likely to come up next by chance. It is therefore a better bet to expect a repeat."

Key phrase: judgment under uncertainty.

Comment author: matteri 06 May 2011 06:24:53PM -1 points [-]

I am not arguing against betting on the side that showed up in the first toss. What is interesting though is that even under those strict conditions, if you don't know the bias beforehand, you never will. Considering this; how could anyone ever argue that there are known probabilities in the world where no such strict conditions apply?

Comment author: matteri 06 May 2011 06:14:22PM *  -2 points [-]

Conrad wrote:

ps - Ofc, knowing, or even just suspecting, the coin is rigged, on the second throw you'd best bet on a repeat of the outcome of the first.

I think it would be worthwhile to examine this conclusion - as it might seem to be an obvious one to a lot of people. Let us assume that there is a very good mechanical arm that makes a completely fair toss of the coin in the opinion of all humans so that we can talk entirely about the bias of the coin.

Let's say that the mechanism makes one toss; all you know is that the coin is biased - not how. Assume that it comes up heads; what does this tell you about the bias? Conrad asserts that it will certainly be biased in favor of heads. How much? Will it always show up as heads? 3 times out of 4? As it turns out, you have no way of knowing.

It could be that it is in fact only 1/3 biased towards heads; then it would be much wiser to bet on tails in the future, no? It could be that it is actually 100 times more likely that tails will come up; you simply can't tell the difference from the first toss.

So let's consider more coin tosses. What if it comes up heads once and then tails 5 times in a row? Could you tell me exactly what the bias is? Is it 5/6 towards tails perhaps? What about 50 tails and 15 heads? In fact, it is still not possible to say anything at all about what the bias is.

Since you probably have a heuristic method of analysis (intuition) you will in time see which side is the best bet; i.e. you'll conclude which side is most likely to be biased and you'll probably be correct - with higher accuracy as the amount of tosses increase. However; there is no logic, rationalism or deduction in the world that could tell you exactly what the bias is. This is true after any integer amount of coin tosses.

Comment author: Morendil 17 February 2011 11:54:51AM 1 point [-]

one of the kids is known to be a boy

That's not the given; it is that "at least one of the two is a boy". Different meaning.

For me, the best way to get to understand this kind of exercise intuitively is to make a table of all the possibilities. So two kids (first+second) could be: B+B, B+G, G+B, G+G. Each of those is equiprobable, so since there are four, each has 1/4 of the probability.

Now you remove G+G from the table since "at least one of the two is a boy". You're left with three: B+B, B+G, G+B. Each of those three is still equiprobable, so since there are three each has 1/3 of the total.

Comment author: matteri 06 May 2011 05:37:24PM 0 points [-]

And in hope of clarifying for those still confused over why the answer to the other question - "is your eldest/youngest child a boy" - is different: if you get a 'yes' to this question you eliminate the fact that having a boy and a girl could mean both that the boy was born first (B+G) and that the girl was born first (G+B). Only one of those will remain, together with B+B.

Comment author: NancyLebovitz 05 April 2011 06:32:56PM 0 points [-]

Is it relevant that humanity doesn't have competent competition?

I wonder how we'd be doing if we were up against coyotes with thumbs.

Comment author: matteri 05 April 2011 10:51:02PM 0 points [-]

First of all; I don't see any apes or monkeys competing with us presently. Also, we are an evolved species. There have certainly been competitors along the way - perhaps said monkeys or apes and most certainly neanderthals as moshez mentioned. We've won though; that is hardly arguable.

Comment author: matteri 05 April 2011 04:14:06PM 9 points [-]

"Anger exists in Homo sapiens because angry ancestors had more kids. There's no other way it could have gotten there."

This is not entirely true - as Boris seems to have noticed. More generally; anything that purely helps survival is certainly more probable to propagate through a species. However, there are other traits that might propagate, such as any of those that are either: a) Not useful nor a burden b) A negative biproduct of something useful, without outweighing the useful