mimasu / mitai usage

Hello,

I have a question on the use of mimasu vs. mitai. 

In lesson 3.2 there is the example:
のんで   みます   か? / nonde mimasu ka? / would you like to try drinking it?

Would it also be correct to say?:
のんで   みたい   です   か? / nonde mitai desu ka?

Does the first sentence literally mean "do you want to try" whereas the second sentence means "would you like to try"?

I'm working on understanding how to apply ~tai at the moment.

Thanks so much!

That is another tough question and I have actually met Japanese people that would use both in a sentence the way you proposed.

The tai form expresses something that you want to do like.

行きたい　I want to go
食べたい I want to eat
飲みたい　I want to drink

Where as the de mimasu is more to try something opposed to a desire to do.

Ok, great - thank you!  That exactly what I thought, so that makes me feel much better :-)