a holdem math problem.

[NYplayer]

Imagine you have AK with no pair on the turn and are out of position, you check and he bets. given the following information how big does the pot have to be to call and how should you play (imagine you have 6 outs to 1 pair).
On the river he will have worse than 1 pair 5% of the time. 1 pair 45% and better than 1 pair 50% of the time.
He will check behind on the river with worse than 1 pair or 1 pair 60% of the time (he will bet worse than 1 pair and 1 pair 40% of the time). he will call a bet from you with 1 pair or better. he folds no pair to a bet.