How would I go about calculating values for distributed percentages?

Question

This might be really simple, but I just can't see it.

I'm working on a game that has 8 items each with a (arbitrary) probability (% chance) of being found:

aluminium = 98.00%
  bismuth =  1.00%
   cobalt =  0.50%
   copper =  0.22%
   nickel =  0.12%
   silver =  0.09%
     gold =  0.06%
 platinum =  0.01%
------------------
    Total = 100%

I want to create a currency for the game. Suppose 200 aluminium = 1 currency. Now I need to figure out how to convert the rest of the items to currency using their given percentages and aluminium 200:1 ratio.

So if I found 1 platinum, how much is it worth in currency?

Answer 1

If 1 currency = 200 aluminium, and aluminium is 9800 times more likely to be chosen than platinum, it might make sense to make 1 platinum be worth 9800 aluminium.

If so, 1 currency = 200 aluminium * (1 platinum/9800 aluminium) = 1/49 platinum. Then 1 platinum would be 49 currency.

For the rest of the metals, just replace the 1/9800 with the appropriate ratio of metal to aluminium.