Two Cards

Alice and Bob have $N$ cards with them. The $i$-th card has the number $A_i$ written on its front, and $B_i$ written on its back. It's guaranteed that $A_i \neq A_j$ for $i \neq j$, i.e, all the $A_i$ values are distinct. All the cards are face-up, so only their $A_i$ values are visible. Alice will choose exactly one card from the $N$ cards, and remove it. After Alice has chosen her card,