This isn't really my field (communication between Pi and Arduino) but I have done a little so I'll give an answer anyway.
RF comms are not noted for their high reliability so messages are usually wrapped in a protocol including a checksum to guarantee integrity.
One of the popular messaging protocols used on Arduinos is Virtual Wire.
I have implemented Virtual Wire for the Raspberry Pi in the form of a Python module. See http://abyz.me.uk/rpi/pigpio/examples.html#Python_vw
The module supports sending and receiving. As goldilocks pointed out with a single transmitter/receiver pair you will have to decide whether the Pi or the Arduino is the sender. That rather begs the question of how you will get any response.