Firstly - that is a whole lot of assumptions you are making simply to justify the given answer. Remember - solutions come from concepts. Not concepts from solutions.
Secondly, assuming page tables are cached - 0.9*(50+100) + 0.1*350 - the problem with this is that you are assuming both levels of page table will be available in the cache at all times, or none will be available. Whereas in reality, it is entirely possible for one level of page table to be in cache, and the other level being a cache miss. This solution does not account for that.
Anyway - if you understand the concept, move on to the next one. Don't try to justify the given answer by any means necessary and risk picking up wrong concepts :)