A question for the mathematically minded jellies, involving statistics and limits.

Say you have a bucket filled with a very large number of red jellybeans and a smaller, but still very large number of green jellybeans. You reach in and grab a bean at random and eat it – as you keep doing this, does the ratio of red to green jellybeans left in the bucket approach 1:1? Common sense is telling me it would, because when you start it is more likely you’ll grab red beans often, thus depleting the supply of red beans faster and evening out the ratio. But, I’m finding it difficult to approach in a mathematical manner. I don’t think I can make the iterations approach infinity because that would assume infinite beans, and I’m having trouble wrapping my mind around there being an infinite number of beans, exactly half of which are red…