Why Airplay mirroring doesnt work on my apple TV with mac book pro using os x mountain lion 10.8.5

AirPlay Mirroring requires a second-generation Apple TV or later, OS X 10.8 or better and is supported on the following Mac models: iMac (Mid 2011 or newer), Mac mini (Mid 2011 or newer), MacBook Air (Mid 2011 or newer), and MacBook Pro (Early 2011 or newer). You can see which Mac you have and which operating system you are using by selecting 'About this Mac' from the Apple menu in the top left corner of your Mac and selecting the 'More Info' button.

If you have confirmed that you meet these requirements, then I would check in system preferences that you have enabled AirPlay.

The following article(s) may help you.

AirPlay Mirroring in Mountain Lion.

Have you restarted the Mac?

Have you powered the Apple TV off and on again?

Have you switched the router off and on again?

Check that both devices are connected to the same network.

These are the usual points where Airplay mirroring fails.

The following article(s) may help you.

Troubleshooting AirPlay

Troubleshooting Wi-Fi networks and connections

Recommended Wi-Fi settings

I'm not sure how you would go on asking for a refund for a problem that isn't the doing of the Apple TV.