Note too that this is a handy way of recycling old internal drives--maybe you recently swapped one out for an SSD and it's sitting in a drawer?--either by slotting them into a dock or mounting them in a drive enclosure. (Mine is from Macally, and Other World Computing sells them too.)
Start building your RAID
Connect your drives then launch Disk Utility (/Applications/Utilities) and click on either of the two disks you want to build into a RAID. Click the RAID tab at the top of the right-hand pane, and name the single drive you'll create in the RAID Set Name field. Ensure the RAID Type dropdown is set to Mirrored RAID Set.
Add drives and set options
Drag the drives you want to use for your RAID setup from the list on the left into the space on the right. Click Options below this space and check the option to have the RAID set automatically rebuilt.
Create the RAID
Click the Create button at the bottom right, double check you have the correct drives specified, then hit the Create button in the confirmation sheet.
Use your new RAID drive for backup
Depending on your system, as soon as the RAID set has finished being built, you might get a prompt to use it as a Time Machine backup; if this is what you want to do, click Use as Backup Disk, but otherwise click one of the other options. For example, you might wish to use a different backup system, such as Super Duper! or Carbon Copy Cloner.
Though there are some optional steps below, you're essentially done now. By backing up to this mirrored RAID drive, you're giving yourself some extra protection; now your main drive can fail and even one of your external backup drives can fail at the same time, and you'll still be able to recover your data. No backup system is guaranteed--all you're doing is mitigating risk with each additional layer of protection you add--but this is a good step in making catastrophic data loss less likely.
Inspect your setup
Before you started this process, you would have had two external drives mounted on your Mac, and showing up on your Desktop and in the Finder Sidebar. Now, it looks like you only have one, but that's because the system is treating those two drives as a single disk. The two drives are still there and connected, but you don't address them independently; you chuck everything at the new RAID set you just created, and the system takes care of mirroring your data to both drives. Have a look in Disk Utility, and you'll see how things are configured.
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