probabillity and math

[wonderousmathemagician]

you're playing a game where you have 45 numbers from which you randomly pick 5 at a time.After 1920 picks, one of the numbers has been picked 245 times.

 

What is the probabillity of that number coming up in the next pick?

In how many picks is it almost certain that that number will come up?

[laminutederire]

How do you pick those exactly?

Actually, I'd try to statistically estimate the probability of that particular number, then try to predict when it will picked up again. You won't ever have absolute certainty though. You have two possibilities, either you say you are wrong at a certain probability in your prediction, or you just want the expectancy?

[CBojorges]

I think it's distribution is hipergeometric. I suppose each pick is independent from the previous one so, for n fixed, the probability of picking it out in the first n picks would be calculated with the inclusion-exclusion formula. 

[laminutederire]

4 hours ago, CBojorges said:

I think it's distribution is hipergeometric. I suppose each pick is independent from the previous one so, for n fixed, the probability of picking it out in the first n picks would be calculated with the inclusion-exclusion formula. 

The issue with your method is that it's incomplete, since you don't know the probability of picking that number

Large number laws can't really be applied with the too few number of picks, so you'll have to statistically estimate the right parameter with the trust interval, then and only can you apply your method

[CBojorges]

15 hours ago, laminutederire said:

The issue with your method is that it's incomplete, since you don't know the probability of picking that number

Large number laws can't really be applied with the too few number of picks, so you'll have to statistically estimate the right parameter with the trust interval, then and only can you apply your method

The parameters of the hipergeometric distribution are the number of elements in each set and the number of elements you pick in each draw. One set has 1 element (the number you're interested in picking) and the other set has 44 elements.  The only problem with my assumption is that I'm not using the sample given. 

[laminutederire]

10 hours ago, CBojorges said:

The parameters of the hipergeometric distribution are the number of elements in each set and the number of elements you pick in each draw. One set has 1 element (the number you're interested in picking) and the other set has 44 elements.  The only problem with my assumption is that I'm not using the sample given. 

The problem is that you don't know the parameters of your probability law, because you don't use the sample. That's what I was talking about when I said one should estimate the value