Golf card game probability? (not homework)

[moonman239]

A and B play a game of golf ( where the player with the lowest score wins). The deck is divided so that 17 cards goes to player A, 17 to player B, and the remaining 17 to the draw pile. Jacks and queens add 10 to the score. Aces add nine, and each numerical card adds a score equivalent to the number printed on that card. Kings are worth nothing.
Three cards are drawn. The cards that B drew are 8,1,and 2. The cards that A drew are 2, 4 and 2. Assuming no cards are drawn from the draw pile, what is the probability that B will win?

 

[moonman239]

Here's an attempt at a solution: Use a binomial distribution to estimate the probability of getting at least 1 good card (that is, a card higher than either the average or the total score of A's sample cards (?)). Using that, calculate the expected frequency. Then use the chi-square test to determine how close the sample is to that frequency. Then calculate the p-value of the test.