Question: Blackjack Table
A standard deck of playing cards contains 52 cards divided equally into four suits: Spades, Hearts, Diamonds, and Clubs. Each suit contains thirteen cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, J(ack), Q(ueen), K(ing), A(ce).
You walk up to the blackjack table at your local casino and ask to be dealt in. You are dealt two cards, the 5 of hearts and the 7 of spades. You see that the dealer also has two cards. One is face down, and the other is the 6 of clubs. You decide to let it ride and hope the dealer busts. The dealer's hidden card is revealed to be the 8 of clubs, making the dealer's hand worth 14 points.
What is the probability that the dealer busts? You may assume that the dealer is usign only 1 deck, and that you have not observed the values of any other cards.