Well, sometimes it appears that those decimal numbers do have a meaning...
First, you want to know what OS X versions you are running where. A simple click onto the Apple in the upper left of your desktop, and then About this Mac, will do.
Then, eventually you want to stress Software Update in the same Apple menu, e.g. to move on from 10.7.4 to 10.7.5.
Finally, it's time to reset your expectations and study the Minimum System requirements of the latest Final Cut, e.g. here, where it states, "OS X v10.6.8 or OS X v10.7.5 or OS X v10.8.2 or later."
Sigh, the wink at the bottom really doesn't help you to get away with the patronism in your answer you know.
I know what OSX systems each of my macs run - 10.6.8 for the mcp and 10.7.4 for the mbair.
I don't want to "stress software update in the same apple menu" and move from 10.7.4 to 10.7.5, because its my understanding from researching reviews on this forum, and from my own experience that updating the operating systems on macs can cause hassle. If I am wrong in this then thats my learning.
Finally, with regards to my expectations, it was a trainer at an applestore , fully aware that I was using these two operating systems, who suggested I upgrade my final cut pro. My expectations were that he knew what fcps compatibilities were.
Finally, what kind of company releases an upgrage system is compatible with an earlier version of its own software (10.6.8), but not with a later one (10.7.4). I do have expectations of apple being better than this.
This is only the second time I've come onto an apple forum to ask a genuine question that foxes me, and the second time I've received the kind of reply that its intended to put one down. Be aware of how your answers come across please.
I hear you, and sorry for stepping onto your feet, but look again how your original post comes across.
Anyway, and aside from your very personal view at and experience with OS updates and upgrades, sometimes software works only on newer, or for a while newest, OS versions. FWIW, that's not only true for Apple software (making Apple no worse "than this"), and it's usually documented in the product description, as is in case of Final Cut. Sorry if you've been misled by an Apple employee - you should go and confront that person with such fact.
Also, it is typically possible to obtain older software versions for use with an older OS. Maybe that's something that the trainer at the Apple Store can help you with at least...