How Does Probability Change as I Draw Numbers from a Barrel?

[idnaui]

Hi
I am not even sure if probability can answer this question but I hope it can.
I have 400 numbers which I draw from a barrel one at a time. I am uncertain as to weather or not all 400 are in the barrel ( they might have been stolen) but I am unable to check.
I am trying to calculate the probability that they are all still there as I draw each number.
I am thinking that If I am unable to draw any, then the probability that they are all there is 0% and if I am able to draw 400 numbers then the probability is 100%. The question is, what comes in between the 0% and the 100%. How does my certainty increase as I draw each number. (each number is known if that helps). Ideally I want to increase certainty with the minimum of numbers drawn
Thanks for any help
Chris

 

[Valkarie]

This is a difficult question to answer, as it is impossible to know the exact probability of an event without knowing all the conditions. However, one way to approach this problem is by calculating what is known as the "conditional probability" of each number being in the barrel, given that you have already drawn other numbers. For example, if you have already drawn 399 numbers and have not had any duplicates, then the conditional probability that the 400th number is still in the barrel is 100%. On the other hand, if you have already drawn 399 numbers and have had three duplicates, then the conditional probability that the 400th number is still in the barrel is 97%. In this way, you can calculate the conditional probability of each number, given the results of the previous draws, and use this to estimate the overall probability that all 400 numbers are still in the barrel. It is worth noting, however, that this approach does not take into account any information about the original distribution of the numbers in the barrel, so it might not give you the most accurate result.