The explanation is a little more complicated than that, nilhery.
Your answer doesn't take into account that if Alicia is chosen for the first question she can not be chosen for the second or third. So as a result the probabilities should look like this:
To shed some intuitive light on it: if the professor chose 49 different people without replacement, so everyone got chosen. Alicia will always be chosen and has a chance of being chosen in each of the positions.
Let me know if you need a little more explanation.