GMAT Sentence Correction (SC) | Re: The professor assumed that Michelle probably have stayed up late last

C is the most appropriate answer here. However Michelle " probably had stayed up" would have been more appropriate as the sentence talks of 2 events and one is before the other . The use of past perfect tense makes more sense than present perfect tense. I.e Michelle fell asleep (later event) after she had stayed up (earlier event) .
Only answer option D uses past perfect tense. However D is wrong as "probably must had"is redundant. Probably