Unable to Reinstall Mac OS X Mavericks

If you have not already tried it, see if Command-Option-R will work on boot, and see if your Mac will reload its software directly from Apple.

If not, then—using another Mac—create a bootable installer on a scratch USB device, and then connect that to your Mac and boot that.

How to create a bootable installer for macOS - Apple Support

If you haven’t prefiously downloaded Mavericks from Apple using your Apple ID, you may have to contact Apple, explain your issue and which Mac you have here, and request a Mavericks redemption code...

But....

Given you’re working with a MacBook Pro 13” Mid 2010, that Mac can boot and run High Sierra and Mojave, and that’s directly available from Apple. That Mac is also upgradable, and can be expanded to 8GB of memory.

Which means that Mavericks is probably not what you want to start with.

Here are direct downloads for the last three macOS releases, from which you can use the appropriate creayeinstalmedia command to build a botable installer on a USB decice on another Mad. That if the Command-Option-R doesn’t get you there...

How to upgrade to macOS Mojave - Apple Support

How to upgrade to macOS High Sierra - Apple Support

How to upgrade to macOS Sierra - Apple Support

Poopoolfafa65 already has a related thread on this: https://discussions.apple.com/thread/8585315

i can not install os x mavericks

also I have the same problem os x 10.11 and 10.10

Your Apple ID never purchased or downloaded Mavericks so it's not available to your.

Use the Internet Recovery option MrHoffman posted above.

Please start your own discussion. Trying to answer several problems in one discussion gets confusing for everyone. A new post would be much more visible.

What happens if you click App Store? Where are you booted into when you get this error? Have you tried the above suggestions, such as Internet Recovery?