Definitional Question about Confidence Intervals My Statistics Homework went as follows
"A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote."
After asking you to make a 95% confidence interval, it then asks you this:
"What is the probability that the true proportion of the professor's students who were registered to vote is in your confidence interval?"
My Stat teacher says this is a trick question and there is no probability. I, however think there is a probability. Who is right here?

Here's the catch: the true proportion is either in the confidence interval or it isn't. That is, you sampled 50 of them, 35 of them said that they are registered, so you get a confidence interval of (for illustration) $(0.6,0.7)$ for the proportion that are registered in the entire class. Now you can imagine actually asking the entire class, and you'll get a number. At this point nothing is random, and nothing is uncertain: your interval is a fixed, specified interval, and the true proportion is a fixed, known number. So the true proportion is either in the confidence interval or it isn't.
Although the true proportion is a fixed number, the confidence interval is random. The precise sense in which the confidence interval is a 95% confidence interval is that 95% of the random intervals generated by samples will contain the true proportion (provided the relevant model assumptions hold). The sample we actually took might or might not be one of the accurate ones.
The idea that we are "confident" that the true proportion is in our given interval only makes sense in the Bayesian framework. But Michael Hardy has already touched on this, so I'll leave that discussion to him.
