TL;DR I finished bachelor's and master's in mathematical finance but want to pursue pure mathematics, particularly in probability theory. I'm not sure if I should apply directly for a PhD. I might apply for a second master's first.
I think the strength of the letter of recommendation (or whether or not there will be a letter of recommendation) from my professors may depend on the program to which I am applying. How should I ask for a letter in this context?
[Details removed following suggestion in comments]
So how might I ask for a letter of recommendation under this context? What I think to ask so far is to first request a consultation asking for advice in applying for graduate programs. At this point I explain I'm not sure if I'm going to apply for a second master's or a PhD. Then of course I ask for a recommendation letter. But how? These are what I have in mind:
Would you be uncomfortable writing me a letter of recommendation?
or
Would you be uncomfortable writing me a letter of recommendation? Would the strength of the letter depend on the program to which I am applying (whether second master's or PhD)?
or
Would you be uncomfortable writing me a letter of recommendation? Would the comfortability of writing the letter depend on the program to which I am applying (whether second master's or PhD)?
or
Would you be uncomfortable writing me a letter of recommendation? Would the strength or comfortability of writing the letter depend on the program to which I am applying (whether second master's or PhD)?