one of the drivers in tomorrows car show cant find a)his or her keys or B)its keys. im going for b.

Answer 1

Drivers are not its. Drivers are people -- so one is referred to as his or her.

Answer 2

I take back my answer. Bobpursley reminded me that "its" could be referring to the car.

So B. is the better answer.

Sorry I mislead you.