[Value = 8 points]
A deck of cards contains twelve cards: two marked with the letter A, two with the letter B, two with the letter C, two with the letter D, two with the letter E, and two with the letter F.
A person plays a game with these cards in the following way. The deck is randomized. The player then draws cards one at a time from the deck. Any time the player has two matching cards in his hand, he discards them. If the player ever has three unmatched cards in his hand, he loses. If he draws every card from the deck without losing, he wins.
What is the probability that the player wins the game?
