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I have a MBP (13” mid 2010) and I wanted to know if the Crucial MX500 or the Samsung EVO 860 work with my laptop?

Yeah you’ll be able to use any 2.5” SATA drive in your MacBook, including the drives you mentioned, no problem.

Your system has a SATA II (3.0 Gb/s) drive interface, as such you need to make sure the drive you put in is able to support this older SATA spec. Only the Samsung SSD offers compatibility Samsung 860 EVO spec sheet You’ll see the interface lists 3.0 Gb/s). Here’s the Crucial MX500 SSD it does not list it.