Probability of guessing the colors of a deck of cards correctly 10 years ago when I was about 15 I sat down with a deck of shuffled cards and tried to guess if the next card in the deck would be red or black. In sequence I guessed 36 cards correctly as red or black, at that point my older bother came in and took told me what I was doing was stupid and I stopped being able to guess correctly. I would love to know what the probability of guessing 36 cards correctly in sequence is? Thank you  

If you're aiming to guess the first 36 cards right with as high a probability as possible, then the best you can do is to choose some sequence of guesses with 18 reds and 18 blacks, and all those sequences are equally likely. 
Each of them has probability 
$\frac{(26\times 25\times 24\times\dots\times9)^2}{52\times51\times50\times\dots\times17}$
$=\frac{26!\times26!\times16!}{52!\times8!\times8!}$
$\approx 2.595\times 10^{-11}$. 
So, the chances are about 1 in 40 billion. 
(Assuming the pack of cards is shuffled)
It's easier than guessing 36 coin-tosses correctly, which would have probability $2^{-36}$ which is about 1 in 70 billion. 
