how you you express this?

[pokerjoker]

How do you express the probability of something happening if it has happened every single trial? Say 20 of 20, or 100000000 out of 100000000?

[AaronBrown]

20 of 20 is the observed frequency of something happening in the past, not necessarily the probability of it happening in the future. Are you asking how to estimate that probability, or just how to represent the observed frequency?

[pokerjoker]

both.

I know its not 100%

[AaronBrown]

The observed frequency in the past is 100%.

To estimate a future probability, you have to consult your prior beliefs. For example, if you watched the sun rise 20 days in a row, you might feel that the chance it would rise tomorrow was 99.999999%. On the other hand, if you watched 20 roulette spins that resulted in a number other than 5, it wouldn't be likely to chance your belief that there is 37/38 chance of getting a number other than 5.

One way to express prior belief is with numbers a and b. If you observe 20 out of 20 successes, you estimate the future probability as (20+a)/(20+b). That means before you observed anything, you thought the probability was a/b. If a and b are large, you had a lot of prior information relative (as in the roulette case). If a and b are small, you didn't know much before you made observations. That might be the case if you were trying something new.

[pokerjoker]

[ QUOTE ]
The observed frequency in the past is 100%.

To estimate a future probability, you have to consult your prior beliefs. For example, if you watched the sun rise 20 days in a row, you might feel that the chance it would rise tomorrow was 99.999999%. On the other hand, if you watched 20 roulette spins that resulted in a number other than 5, it wouldn't be likely to chance your belief that there is 37/38 chance of getting a number other than 5.

One way to express prior belief is with numbers a and b. If you observe 20 out of 20 successes, you estimate the future probability as (20+a)/(20+b). That means before you observed anything, you thought the probability was a/b. If a and b are large, you had a lot of prior information relative (as in the roulette case). If a and b are small, you didn't know much before you made observations. That might be the case if you were trying something new.

[/ QUOTE ]

That would mean that without prior information that it is 100% likely then? Also if something only occured once and the result was x, then x would be 100% likely. Maybe my question is somewhat abstract. Any other answers?

What if there was a computer program and whenever u clicked the screen it displayed a number (you have no idea what the algorhythm is)

the first 1000 times it displayed the number 1. Is there a way to represent the odds (given our information) it will display 1 again?