A student ran oit of time

Question

A student ran out of time on a multiple choice exam and randomly guessed the answers to two problems.  Each problem had 4 answer choices - a, b, c, d - and only one correct answer.  What is the probability that she answerer both questions correctly?  Write answer as a fraction in simplest form.

Answer 1

The probability of the student answering the first question correctly is 1/4. That is also the probability that the student guesses the correct answer to the second problem. The probability of guessing the correct answer to both problems is 1/4 * 1/4 = 1/16.