A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d, e - and only one correct answer. What is the probability that she answered neither of the problems correctly? Write your answer as a fraction in simplest form.

We can break this down:

The student has a one out of five chance of getting a correct answer, and a four out of five chance of an incorrect answer. We can express the students odds of getting one incorrect answer as 4/5. In order to get the odds of two wrong answers, we need to multiply this answer again by the odds of choosing a wrong answer. Therefore:

The odds of one wrong answer = 4/5

The odds of two wrong answers = (4/5) * (4/5) = 16/25 chance of getting both of the questions wrong.