In a test for ESP (extrasensory perception), a subject is told that cards the experimenter can see but he cannot contain either a star, a circle, a wave, or a square. As the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. A subject who is just guessing has probability 0.25 of guessing correctly on each card.
(a) The count of correct guesses in 20 cards has a binomial distribution. What are n and p?
(b) What is the mean number of correct guesses in many repetitions of the experiment?
(c) What is the probability of exactly 5 correct guesses?