A student has just been given a 10-problem multiple choice quiz in his history class. Each problem has five choices of which only one of those choices is correct. Since he has not attended class recently, he doesn't know any of the answers. Assuming that he guesses on all 10 problems, find the following:
a) What is the probability that he will answer all ten problems incorrectly?
b) What is the probability that he will answer at least one of the problems incorrectly?
c) What is the probability that the first problem answered correctly is the second problem he answers?