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Old 03-14-2012, 04:20 PM   #81
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Originally Posted by LegionOnomaMoi View Post
... At no point did I say "what is the relative or expected probability of obtaining a certain number of heads and tails in 40 coin tosses?"...
Your statement is RECORDED.
[snipped my quoted post as it is posted in full below]

It is clear, common sense, that people would EXPECT a MIX of Heads and Tails and NOT the very same identical mix or ALL Tails.
That's true. But once again, that wasn't the question. You neatly cut off the actual question, so I'll post what I said about the coin toss problem in full, rather than your neatly edited version (emphasis added):
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Originally Posted by LegionOnomaMoi View Post
A fair amount of research has demonstrated how badly "common sense" and our natural reasoning abilities fall apart when it comes to logic and probability. For example, when a coin is tossed many times, we don't expect exactly 50% tails, but we do expect something that approximates that. In other words, we would expect a coin toss that looks like this:

HHTHTTTHTTHHTHTHTTHHTTTTHHHTHHHTTHTHTHTTTHTT

(where H is heads and T is tails and thus the above represents a mix of both) rather than this:

TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT

So, assuming that both of the above have the same number of "tosses" (I didn't count) most people would say that the first is far more likely than the second, as the second is CLEARLY highly improbable.

Only they would be absolutely wrong. The probability of both tosses (again, assuming I series has the same number of tosses) is exactly equal.
Note that I never said anybody was wrong for expecting a mix. Where in this post did I say where and why what "most people" say is wrong? It wasn't because they are wrong for understanding that a mix of heads and tails is more likely than all tails. I gave the results of 2 specific series of tosses, and then I said "most people would say the first is far more likely than the second. That's where they are wrong.

Moreover, this wasn't the post your responded to. When asked for clarification, I simplified:
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Originally Posted by LegionOnomaMoi View Post
A coin is tossed 40 times, without any particular streaks, with the following results:

HHTHTTTHHTHTHHTTHTHTTHTTHTHHHTHTTTHHTTHT

Another coin is tossed 40 times, and ends up all tails:

TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT

Which is more likely?

The probability of either is exactly equal.
This was the post your first responded to with the following:
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Originally Posted by aa5874 View Post

So probability is meaningless or has NO real significance to determine history if what you say is true.
In this post, I said nothing about what people expect to find. I simply gave two different results and asked which is more likely, and then answered. The answer is correct, yet either you know you are wrong and obstinately refuse to admit it, or you still really don't understand why you are wrong (perhaps because you aren't taking the time to read carefully and think about what I said in the post you originally responded to along with subsequent explanations).

You continue to talk about a problem I never posed and an question I never asked. I never asked whether a mix is more likely, nor did I ever say people who think so are wrong.

They are wrong because they do what it appears you continue to do: they can clearly see that one toss is a mix, and the other toss isn't, and they know the second one is very unlikely, so they miss the fact that I'm not asking whether a mix is more likely, but presenting 2 specific sequences of heads and tails. To compute the probability of any particular sequence given 40 fair tosses, you multiply the probability of each toss (.5) 40 times.

Any sequence you actually get from a n fair tosses has the same probability every other sequence you could possibly get has.


Quote:
A MIX is more likely than all heads or tails when the mathematical probability is .5
I never said it wasn't, I never said people were wrong for thinking this, and in the post you first responded to, I never even said anything about a mix or what people expect.

I don't get why you are still on the fact that for any n tosses you expect a mix in general or something that approaches/tends towards .5 H and .5 T. That was never the problem/question posed. I always gave 2 specific sequences.

So I'll ask again: given a series of n coin tosses, where n is any positive integer, how do you compute the probability of the sequence of heads and tails you actually get from those n tosses?
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Old 03-14-2012, 08:05 PM   #82
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Here's the problem. You keep dealing with the wrong question. So I'll let's make it simple. If I toss a fair coin 4 times, what is the probability that I will get four heads (HHHH)?
In order to allow you to show me up with your great knowledge, I will offer 1 in 16 attempts = 6.25%. (1/2 * 1/2 * 1/2 * 1/2). Now, I humbly await your disdain and wrath for not being as smart as you.

DCH

PS: Isn't San Bernardino a little industrial for a man like you? You should be in the San Francisco Bay area, maybe Berkeley ... maybe even ... Palo Alto.


LOL now thats just mean right there!!!! :devil1:
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Old 03-15-2012, 12:08 AM   #83
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So I'll let's make it simple. If I toss a fair coin 4 times, what is the probability that I will get four heads (HHHH)? [/B]

How do you know (in advance) that you are dealing with a fair coin?

I certainly would not regard the "Early Christian literature" as a fair coin. It's possibly quite corrupt. It has a H and a T. The head is the canonical head of the canonical Jesus, while the tail is the noncanonical imprint of the gnostic heretics. The Vatican and all Believing Apologists can flip this coin all day for centuries, but the result is always heads.
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Old 03-15-2012, 01:49 PM   #84
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Now if I only got his city right :constern01: He's prolly at MIT where his knowledge of classics would be most useful, but he could be at Yale or Harvard.

DCH

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Originally Posted by DCHindley View Post
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Originally Posted by LegionOnomaMoi View Post
Here's the problem. You keep dealing with the wrong question. So I'll let's make it simple. If I toss a fair coin 4 times, what is the probability that I will get four heads (HHHH)?
In order to allow you to show me up with your great knowledge, I will offer 1 in 16 attempts = 6.25%. (1/2 * 1/2 * 1/2 * 1/2). Now, I humbly await your disdain and wrath for not being as smart as you.

DCH

PS: Isn't San Bernardino a little industrial for a man like you? You should be in the San Francisco Bay area, maybe Berkeley ... maybe even ... Palo Alto.


LOL now thats just mean right there!!!! :devil1:
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Old 03-25-2012, 07:13 AM   #85
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From the blog of Joseph Hoffmann:

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Several colleagues will be responding on this site in a week to claims made by atheist blogger and amateur "logician" Richard Carrier concerning the historical Jesus (contra Bart Ehrman) and his abuse of Bayes's theorem. In the meantime, this from 2011.

http://rjosephhoffmann.wordpress.com/2012/03/25/4716/
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