Expected numbers of cards of a last color remaining

[WMDhamnekar]

TL;DR

Expected numbers of cards of a last color remained if all cards of other 2 colors in a deck of 100 cards of 3 colors are drawn randomly one by one.

In a deck, we have 35 green cards, 25 blue cards and 40 red cards. The cards are shuffled randomly. And the cards are drawn one by one without replacement until only one color remains in the deck. What is the expected number of cards remaining?

I am working on this question. If any one knows the correct answer may reply with all the explanations.

 

[Dale]

That would be the same as drawing N cards without replacement that match the first color.

 

[FactChecker]

That would be the same as drawing N cards without replacement that match the first color.

That was my first thought, and it still might be valid. But an abundance of one color certainly changes the odds of the last card whereas that is not true for the first card. I don't see a clear way to handle that.

 

[Dale]

That was my first thought, and it still might be valid. But an abundance of one color certainly changes the odds of the last card whereas that is not true for the first card. I don't see a clear way to handle that.

My thinking was that when you have shuffled a deck there is no statistical difference between drawing from the top of the deck and drawing from the bottom of the deck.

 

[Dale]

I did a Monte Carlo simulation of 100000 shuffles with drawing from the front and got a mean value of 1.514 and a simulation of 100000 shuffles with drawing from the back and got a mean value of 1.517