A student has just been given a 10-question multiple choice quiz in his history class. Each question 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 questions, find the following:
a) What is the probability that he will answer all ten questions incorrectly?
b) What is the probability that he will answer at least one of the questions incorrectly?
c) What is the probability that the first question answered correctly is the second question he answers?