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I have studied it before but I forgot the name.

It is like when the possiblity of something happens is so small, but you created the experience so so many times, then the probability of that thing to happen is high.

It is like: the possibility of having a life in a planet is $2\times10^{-17}\%$ but there are $5\times10^{19}$ planets, so the probablity of having a life becomes higher.

I know i did a wrong maybe example, but i am asking about the name of that field (or theory)

Michael Hardy
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Marco Dinatsoli
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    You might get better responses if you format your post a little better. Use capitalization and spell words out ("you" instead of "u"). –  Jul 27 '15 at 20:24
  • Are you referring to the Law of Large Numbers? The wording of your example is not quite correct (the probability of an event does not 'become higher' under such circumstances), so I thought I would ask in a comment rather than risk posting an irrelevant answer. – Will R Jul 27 '15 at 20:30
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    I'm pretty sure this isn't about the laws of large numbers - it sounds to me like Marco is thinking of expectation, but it's hard to tell. – preferred_anon Jul 27 '15 at 20:37
  • An event with very small but positive probability will eventually occur almost surely infinitely many times if the experiment is repeated enough times. The Borel-Cantelli Lemma may be related: https://en.wikipedia.org/wiki/Borel%E2%80%93Cantelli_lemma#Converse_result – jdods Jul 27 '15 at 20:39
  • @DanielLittlewood: What makes you so sure? The second sentence in the question is quite close to saying 'even if the probability of a particular experimental result is small, we can still expect it to happen at least once if we perform the same experiment a large number of times', which, to my mind, is an informally stated consequence of the LLN. The concept of expectation is not really enough: it is the LLN which allows us to expect its occurrence, given enough trials. – Will R Jul 27 '15 at 20:54
  • @WillR I think I might agree with you. The reason I thought this wasn't about the LLN is because of the part "so the probability of having a life becomes higher", but of course in the law of large numbers your actual probability of finding life on a particular planet doesn't change. I think I suggested expectation in the same sense you suggest the LLN, and I think Borel-Cantelli actually captures the concept better than either of them. – preferred_anon Jul 27 '15 at 20:59
  • @DanielLittlewood Borel-Cantelli may well be relevant, but it seems too technical to be the sought response (no offence meant to Marco here, of course; I just feel that if such a technical result from measure theory is really being referred to, then it is unlikely that the question would be couched in such a down-to-earth setting as having actual numbers representing the probabilities!). – Will R Jul 27 '15 at 21:09
  • @WillR I agree that the theorem itself is too hard, but the spirit of it (e.g. if you flip a coin a large number of times, the likelihood of getting 0 heads is very small) is pretty straightforward. An intuitive argument for it could be very simple. – preferred_anon Jul 27 '15 at 21:20
  • thanks for all your contribution, but it seems the example of the life outside is not according to the laws of large numbers, i hope u help me out here – Marco Dinatsoli Jul 28 '15 at 00:01

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Possibly you're thinking of the Poisson distribution.

Suppose you have a one-in-$1{,}000{,}000$ chance of success on each trial, and there are $3{,}600{,}000$ trials. The expected number of successes is then $3.6$. If we ask for the probability that there are exactly $5$ successes, we get $$ \frac{3.6^5 e^{-3.6}}{5!} = \frac{3.6^5 e^{-3.6}}{120} \approx 0.13768. $$ Ladislaus Bortkiewicz's book The Law of Small Numbers, published in 1898, used the Poisson distribution to model the number of soldiers in the Prussian cavalry each year killed by being kicked by a horse. He also applied it to data on suicides by pre-pubescent children.

Michael Hardy
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It seems like you may be referring to the Law of Large Numbers. The Wikipedia page linked to gives a good explanation, from what I can see. See also:

Community
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Will R
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  • i don't think that is the one i am looking for, i am looking for a theory that says that even if the probability for one shot is small, doing that shot too too too too too many times, i will end up with even a bitter probability or with a sure probability – Marco Dinatsoli Jul 28 '15 at 00:07
  • So, you mean to say you're looking for a description of a situation in which the probability of an event is affected by the number of trials so far? For example, if I flip a coin repeatedly, and every time I get a 'tails' result I add some weight to the 'tails' side of the coin so that the coin is more likely to come up 'heads' next time I flip it? – Will R Jul 28 '15 at 00:26