In a game where card color determines each player's team, there are 5 shuffled cards -- 3 blue and 2 red -- and 4 players. The first player chooses one card from the pile and keeps it. This goes around until each player has chosen a card. At the end, the one remaining card gets discarded. In a single round of the game, what is the probability that one red card is chosen? What is the probability that both red cards are chosen? Please explain your methodology.
So far, I (no mathematician) have reasoned that this problem requires some sort of Bayesian decision tree. For the first person, the probably of red is 40%. The second person's card depends on what the first player drew. If the first player drew red, then the second player has a 25% chance of drawing red; otherwise, s/he has a 50% chance of drawing red. This continues on. However, I'm having trouble generalizing this into a function of N cards, N-1 players. Additionally, I'm not sure how to figure the probability of 2 reds. Probability of 1 red is simpler.