A math quiz has 3 multiple choice questions and each question has 3 choices. If a student has to guess (and is not able to remove any of of the incorrect choices) what is the probability that the student answers all of the questions correctly?
Since there are 3 choices for each question, and the student must guess for each question, there are 3^3 = 27 possible outcomes for the student's guesses.
Out of these 27 possible outcomes, only 1 outcome will result in the student answering all of the questions correctly.
Therefore, the probability that the student answers all of the questions correctly is 1/27. Answer: \boxed{\frac{1}{27}}.