Physical skills and trades like plumbing will likely last the longest as a profession, because it is going to take time to be able to develop a robot that is able to negotiate all the different conditions and positions that are required.
Are these not already in practice today? Like there are now sophisticated AI machines that might wipe out major lucrative skills, well if maybe I am guessing wrong but I fear it might soon be in reality. There are building more crazy devices out there. But again there is always a edge on humans capacity over machines, they act base on programmed rules not precision, so a minor mistake can be continually done if not quickly adjusted and again machine do not have emotions or thinks in probability. Thanks for this masterpiece @tarazkp
A robot to fix your toilet? They don't exist. Neither are there robots that pull wiring through a house. Not yet at least.