In either case (solo vs pool), the luck factor would be the same, amirite?

Is this statement accurate "I am just as likely to find a block solo mining, as I am in a pool." ?

I understand that the pool rewards everyone trying contributing by sharing out the reward block. And that you could probably go for years solo mining and not see any return. But its equally possible, though improbable, that you could find / solve a block in your first five minutes.