Question from Poker, Gaming, and Life

[gmcarroll33]

On page 123 dealing with possible hand combinations and all David presents the following question for us to figure out on our own. Help me out and tell me if I did the problem correctly.

You are dealt QQ. Flop comes Q-J-10 leading you to believe your opponent has either a big pair, jacks or better, an AK type hand, or AQ suited. What is the chance I flopped the best hand.

With a Jack on board there are only 3 combinations of JJ in his hand he can have. There are still 16 AK combinations. 6 AA combinations, 6 KK combinations, and only 1 AQ suited combination left. So that totals 31 total combinations he could have.

So of the 31 combinations he could have I can beat 16 of them. All except AK, making me a 16/15 favorite, or 4/3 favorite. Is this correct? If not explanation on where I went wrong is appreciated.

Basically is this a coin flip situation. I came up with 31 divided by 15 equals about 48% so it's almost a coin flip.