I'm looking for a series/function for this card game statistic. I'll post a specific case to start but I'm looking for the general case.
Ex. You have a 10 card deck of 5 blue cards and 5 red cards. And you preform this action. Draw a card if it is red preform this action again.
I know this is #cards drawn on average = [1+(5/10)+(5/10)(4/9)+(5/10)(4/9)(3/8)+(5/10)(4/9)(3/8)(2/7)+(5/10)(4/9)(3/8)(2/7)(1/6)]
But I am looking for a function for the general case with A deck of N blue cards and M Red cards.
Thank you very much for your Consideration.