LegionOnomaMoi

Wow. Clearly I have to explain this a different way for you. I'm talking about specific sequences.

I toss a coin once. The probability that I will get heads or tails (given a "fair coin" or "fair toss") is 50/50, or .5. I toss two coins. What is the probability that I will get HH? It's .5*.5=.25 or a 25% chance. What about the probability that I will get HT? The same. How about TT? The same.

Now I toss a fair coin three times. What is the probability that I will get HHH? .5*.5*.5=.125 or a 12.4% chance. What about HTH? The same. What about TTT? The same. What about HTT? The same.

Now I toss it four times. The probability that I will get HHHH is .5*.5*.5*.5=.0625 or a 6.25% chance. That is also the probability that I will get HTHT, or THTH, or TTTT, or TTTH, or any other possible sequence from four coin tosses.

Each time I add a toss to my number of tosses, I compute the probability by multiplying by an additional .5 to the number of .5's I multiplied in the last series of tosses.

So if I toss 40 coins, I compute the probability by multiplying .5 40 times (.5^40). It's 9.094947017729282379150390625 × 10^-13. This is true no matter what actual sequence I get, including and
TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT.

aa5874

You do not understand the difference between what is expected and the mathematical probability.

The mathematical probability for 'heads' or 'tails' of a coin toss is .5.

It is EXPECTED that Forty consecutive coin tosses would produce a RANDOM quantity of heads and tails that APPROACHES the mathematical probability of .5.

There is ZERO expectation for forty consecutive coin tosses to produce all heads, all tails or a fixed quantity of heads or tails when the mathematical probability is .5

Field tests and experiments of 40 consecutive coins tosses will TEND to support the mathematical probability of .5

David Deas

Stick to the liberal arts because clearly you do not understand mathematics. In the case of a coin toss the probability of any particular sequence occurring in 40 flips is equal.

youngalexander

The 'coins' are of course always assumed to be 'fair', ie. P(H) = P(T) = 0.5

Suppose that we ask a slightly different question. If a sequence of fair coin tosses are made, which of
HHTH...
and
TTTT...
will occur first? The answer is HHTH... by a wide margin!!
Counterintuitive
Probabilities in Coin Tossing

Probabilistic methods require careful attention to detail.

Carrier does not claim that Baysian methods are mandatory. A correctly executed logical argument will serve as well. What he does claim is that the two methods are equivalent. Further, that a Baysian approach forces one to think very carefully concerning the precise question being asked and requiring that all the alternatives and their priors are taken into account. It is easier to overlook this with a purely verbal method.

aa5874

You don't understand how to apply mathematical probabilities.

The mathematical probability FOR heads or tails OF COIN TOSSES is .5 and FIELD TESTS of Coin Tosses will produce results that support the mathematical probability.

In other words, if all the people who post on this thread individually make 40 consecutive coin tosses it will be seen that EACH poster will come up with a result of Random quantities of heads and tails that APPROACHES the mathematical probablility of .5.

LegionOnomaMoi

How is this still a problem? 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?" Do you know how to compute probabilities for any n independent "events" when the probability function of each event is known?

You are talking about expected probability. Given any n coin tosses, the expected probability E(x) is .5 As n grows larger, the more likely it is we will actually get that result.

All of this is completely and utterly irrelevant given what I asked. I didn't ask "what would you expect given 40 coin tosses?" I said:
You are talking about relative or expected probability. I asked which of the above two sequences of 40 tosses was more likely. In order to answer this question, you need to compute the probability. For a single fair coin toss, the probability of obtaining heads or tails is .5. However, if I ask you what is the probability of obtaining two heads given two coin tosses, the way you compute this is by multiplying the probability of each independent toss. It's the same with any known probability function for independent "events." If I ask what is the probability of drawing two aces from a pack of cards with replacement (i.e., after I draw the first ace, I put it back in), I would get the answer by multiply 4/52 by 4/52. The probability of obtaining each ace is 4/52, so as long as I replace the cards the way I answer the question of obtaining two aces (which are two seperate "events") is by multiplying the probability of obtaining each.

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)?

tanya

Thanks for this comment, well written, in my opinion.

I would, however, prefer to take the other side of this particular coin toss. I disagree with anyone who writes that mathematical techniques can be applied to the study of our most ancient documents, underlying the origins of Christianity, for the purpose of identifying authenticity.

Most (in my opinion) theological disputes arise, because of different texts, outlining contrary views of "the correct" position on any issue.

Discovering how and why the earliest sects split away from one of the several versions of Judaism, extant 2000 years ago, is a challenge which, again, only in my opinion, can not be addressed by cloaking an investigation of our oldest documents, in garments woven from mathematics.

Logic is overrated in this field of inquiry, and cannot trump archaeology. Honesty is a far more important attribute for any investigation of these ancient sects and their supposed doctrines.

Where mathematics can play a role in this process, is (not analyzing arguments) creating, in tabular layout, Greek word frequency in various copies of the same document, in hopes of identifying phylogenetic trees, to suggest a plausible revision history of the documents.

Plausibility then, would come, NOT from application of Bayes' theorem (nor from Fourier analysis of the tree), but from existence of a credible chart, illustrating which particular document had felt the touch of the quill first.

LegionOnomaMoi

So you've said. However, your argument amounts to "show me how this technique may be used, but if you do I won't look at your example or dispute anything about it, I'll ignore it and continue to asert my claim about the technique without understanding it."

I provided you a link with an example Carrier wrote showing how Bayes' theorem can be used. If you want to say "we can't use bayes'" then you have to deal with how it is used, and critique that, not blindly assert we can't use it without knowing how it is used.



well that explains a lot.



Archaeologists, like all historians, use things like "inference" and "deduction" and "probability" to interpret their findings. In other words, they use logic. It's called reasoning.

DCHindley

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.

aa5874

Your statement is RECORDED.

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.

A MIX is more likely than all heads or tails when the mathematical probability is .5