Probability of selection in a simple random sampling over a series

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I'm trying to figure out the probability of any one person not being cold called in my law school class.

There's about 70 students in the class, we have 27 total classes in the semester, and before every class the professor makes a randomized list of the students (assuming true random), cold calling them in that order. There's about 3-4 cold calls every class, so lets say 90 total for the semester.

I'm awful at math (law school), but wanted to know the probability of any one person (hopefully me) never being called on during the semester.

Also the formula for figuring this out in future classes would be nice. I don't even know enough math to figure out the correct words to google it.