Question: Binomial Probabilities-Multiple choice quiz

Richard has just been given a 10 question multiple-choice quiz for his history class. Each question has 5 answers, of which only one is correct. Since Richard has not attended class recently, he doesn’t know any of the answers. Assuming that Richard guesses on all 10 questions, find the indicated probabilities-

a) What is the probability he will answer all questions correctly?

b) What is the probability he will answer all questions incorrectly?

c) What is the probability that he will answer at least one of the questions correctly?

d) What is the probability that he will answer at least half the questions correctly?