In a game of blackjack, the player and the dealer are both dealt two cards. One of the dealer's cards is dealt face up so that the player gets to see it. Suppose you (as a player) are dealt a 10 and a 6 and you observe that one of the dealer's cards is a 7.

Given the three observed cards, what is the probability that the dealers cards total more points than yours (before any additional cards are drawn)?

Refer to given Exercise for a description of the point values of various cards in blackjack.

Exercise

In the game of blackjack, Aces are worth 11 points (or they can also be counted as 1 point, but for the sake of this problem, we will only count them as 11 points), 10s, Jacks, Queens, and Kings are all worth 10 points and the other numbered cards are worth their face values (i.e., 2s are worth two points, 3s are worth three points, etc.). The suit of the card does not matter.

(a) Find the probability of being dealt a two-card blackjack hand worth a total of 18 or more points?

(b) Find the probability of being dealt a two-card blackjack hand worth a total of no less than 12 points and no more than 17 points?