Coin toss odds?
Satt, I think my question to my teacher would be how many tosses must be made to be able to prove the 1/2-1/2 coin toss odds? I doubt that anyone can set a finite number without resorting to Prime Numbers. For example, for finding all the small primes, say all those less than 10,000,000,000; one of the most efficient ways is by using the Sieve of Eratosthenes (ca 240 BC):
-----BumbleBeeBoogie
PROBABILITY:
Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0. An event with a probability of 1 can be considered a certainty: for example, the probability of a coin toss resulting in either "heads" or "tails" is 1, because there are no other options, assuming the coin lands flat.
An event with a probability of .5 can be considered to have equal odds of occurring or not occurring: for example, the probability of a coin toss resulting in "heads" is .5, because the toss is equally as likely to result in "tails."
An event with a probability of 0 can be considered an impossibility: for example, the probability that the coin will land (flat) without either side facing up is 0, because either "heads" or "tails" must be facing up. A little paradoxical, probability theory applies precise calculations to quantify uncertain measures of random events.
In its simplest form, probability can be expressed mathematically as: the number of occurrences of a targeted event divided by the number of occurrences plus the number of failures of occurrences (this adds up to the total of possible outcomes):
p(a) = p(a)/p(a) + p(b)
Calculating probabilities in a situation like a coin toss is straightforward, because the outcomes are mutually exclusive: either one event or the other must occur. Each coin toss is an independent event; the outcome of one trial has no effect on subsequent ones. No matter how many consecutive times one side lands facing up, the probability that it will do so at the next toss is always .5 (50-50). The mistaken idea that a number of consecutive results (six "heads" for example) makes it more likely that the next toss will result in a "tails" is known as the gambler's fallacy, one that has led to the downfall of many a bettor.
Probability theory had its start in the 17th century, when two French mathematicians, Blaise Pascal and Pierre de Fermat carried on a correspondence discussing mathematical problems dealing with games of chance. Contemporary applications of probability theory run the gamut of human inquiry, and include aspects of computer programming, astrophysics, music, weather prediction, and medicine.
Read more about it at:
> More information is provided in an "Introduction to Probability."
> The Interactive Mathematics Miscellany and Puzzles provides a probability tutorial.
> MathPages provides more advanced tutorials in its section on "Probability and Statistics."
> Clarkson University's "The Probability Web" is a compendium of online probability resources.
The usual probability of (1/2, 1/2) for (H, T) of tossing a coin is simply an assumption. Its plausibility is backed by the "Law of Large Numbers", though the theorem, in turn, is proved under the hypotheses of Probability theory and Analysis which contain arithmetic in an essential way, and the consistency cannot be proved.
(I was teaching probability calculation for students, too. BBB, you could embarrass me by asking a question, but you might be obliged to pay for it. A few occasions can be provided as a trial period.)
Now wait a minute guys;
This stuff is waaaaaaaaaaaaay beyond BushBaby!
What's it doing here;
well, actually, I guess there was a fifty/fifty chance it would turn up
And btw why should we be specifically concentrating on his fatal ignorance of evolution? The topic (his ignorance) has sooo much scope.......
Europe
As an anti-war french, I fully agree with what you're saying about Bush.
But I wonder about the meaning of his action. In the view of history, I mean. Will it be seen, in the enxt centuries, as the last, desperate try of western civilisation to lead the world ? I remember having read once that "power always goes West", from Asia to Europe, from Europe to America, and now from America to Asia ? I just wanted to know your opinions about this.
I think the only thing you can count on "always going west" is daylight (the apparent movement of the sun).
As far as power is concerned, I think it will hover around North America for a while, unless the U.S. insists on continuing to shoot itself in the foot, and septisaemia sets in.
