You have Kc Kd, and $1300 in front of you. You raise to $50, and your opponent in the small blind, who also had $1300 when the hand began, re-raises to $300. You believe she has either QQ, AK, or AA. The flop comes Jc Ts 3d, and your opponent goes all-in for $1000. Based on her all-in bet, you now believe that she has either QQ or AA, and suppose that you believe that she is equally likely to have either of these two pairs.

a) If she has QQ, what is your probability of winning the hand?

b) If she has AA, what is your probability of winning the hand?

c) Should you call? (Let X = the number of chips you will have after the hand. Calculate the expected value of X if you call, and compare with the expected value of X if you fold.)

I’ve been trying to solve this problem but with no luck. So far I’ve listed

(K,9),(8,9),(Q,2-10),(Q,Q) as cards that your opponent could use to win. Now I have no idea how to proceed from here.