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 just guess red or black with a 50/50 chance, without taking into account that memory of the previous cards can make a guess more accurate, then the probability of guessing 36 cards in a row correctly is:
$$\left(\frac 12\right)^{36}$$
For comparison, if all 7.125 billion people in the world were to attempt this, the probability that anyone in the world would succeed is
$$\left(\frac 12\right)^{36} ~~\times~~ 7.125 \times 10^9 = 10.4\%$$
Which makes your story somewhat unbelievable.
