What is the formula for ranking combinations of two sets of numbers?

[Tegga]

Greetings Mathlings,

I am Tegga from a different planet, where the knowledge of maths is very ordinary. I need your help. I am looking for a formula to rank 2 sets of numbers. The first set is, say 1 to 12 - but it could be anything from 1 to a maximum of 30. The second set is again, say 10, but could be anything from 1 to 30.

If I combine the 2 lists in every possible combination, eg 1-1, 1-2...12-10. There would be a total possible 120 combinations in a list of 10 and 12. The combination of 1-1 is the most likely combination, while the combination of 12-10 is the least likely.

What I am looking for is a formula which will give a weighting of the probability of any particular combination, so that the whole 120 combinations have some sort of probability rating. The problem is that as we move down the list, the likelihood of each combination gets less, but not in a linear fashion.

Is there such a formula, do you know?

Thanks

tegga

 

[CompuChip]

How do you mean, 1-1 is the most likely combination?
Given the sets {1, ..., 12} and {1, ... 10}, isn't 1-1 as likely as 12-10?
Or do you mean that we consider all combinations from the sets {1, ..., n} and {1, ..., m} simultaneously (in which case, 1-1 occurs for all n and m, while 12-10 only occurs for n > 11 and m > 9 making it less likely)?

 

[Tegga]

Thanks for your reply -

Lets say that the numbers {1 - n} are ranked in the order that is most likely to occur, as are the numbers in the second list {1 - m}. In combining the 2 lists, eg {1-1}, given that they are the highest ranked, ergo the most likely, numbers in each of the lists, this combination is the most likely to occur. Given that {12 - 10} are the lowest ranked numbers in each of the lists, this combination, while possible, is the least likely to occur.

Does that make sense?

Cheers

 

[gsal]

I think you simply need to multiply the probabilities.

For as long as the series of listed events in list 1 are independent of the series of events in list 2.

For example of instead of numbers {1, 2, 3} and {3, 5, 8, 11}, we list their probabilities {0.5, 0.3, 0.2} and { 0.4, 0.3, 0.2, 0.1} ...then

0.5x0.4=0.2
0.5x0.3=0.15
0.5x0.2=0.1
0.5x0.1=0.05
0.3x0.4=0.12
0.3x0.3=0.09
0.3x0.2=0.06
0.3x0.1=0.03
0.2x0.4=0.08
0.2x0.3=0.06
0.2x0.2=0.04
0.2x0.1=0.02

 

[Tegga]

Hmmmmmmmm

I'll have a look and see if I can do that...

Thanks

 

[awkward]

I'm not sure of what you want, but you might take a look at

http://en.wikipedia.org/wiki/Spearman's_rank_correlation_coefficient

 

[Tegga]

Thanks,

I don't think that is what I'm after...what I could understand of it that is...Remember, I'm from a different planet. But...er...ummm..thanks anyway