## NP-complete Proof

I have the following problem which I guess it is NP-complete, but I cannot find a good existing NP-complete problem for reduction.

There are three devices A, B, and C. Both A and B have a packet to send to C within N time slots. In each time slot, if only A sends its packet, C will receive A's packet with probability p_{a}; if only B sends its packet, C will receive B's packet with probability p_{b}; if both A and B send in the same time slot, C will receive neither of them.

The objective is to create a transmission schedule with length of N time slots, so that the probability for C to receive both packets is maximised? For example, for N=5, a transmission schedule looks like this: {A}, {B}, {A}, {AB}, {AB}. In slot 4 of this example, both A and B are scheduled. If both of them failed in the previous 3 slots, they will both send and C will not receive neither of the two packets. If B has succeeded in slot 2 and A fails in the first 3 slots, only A will transmit in slot 4, and C will receive A's packet with probability p_{a}.

Any suggestion?