A man has been guessing the colors of cards drawn from a standard deck. During the first 50 draws, he kept track of the number of cards of each color. What is the probability of guessing the color of the fifty-first card?
I’m not positive about this, but here goes:
There are three possible events: 2 black cards, 2 red cards, or 1 of each.
The probability of two cards being black is .5*25/51 = .2451
The probability of two cards being red is .5*25/51 = .2451
The probability of two cards being the same color is therefore .4902
In other words, about half the time, the guesser will always know for sure what card is next.
The probability of two cards being of different colors is 26/51 = .5098
The probability of guessing wrong is the probability of getting two different colored cards (.5908) times the probability of choosing the wrong color (.5): .5098(.5) = .2549
Therefore the probability of guessing correctly is 1- .2549 = .7451
