A teacher gives a four-question unannounced true-false pop quiz, with two possible answers to each question.
a. Use a tree diagram to show the possible response patterns, in terms of whether any given response is correct or incorrect. How many outcomes are in the sample space?
b. An unprepared student guesses all the answers randomly. Find the probabilities of the possible outcomes on the tree diagram.
c. Refer to part b. Using the tree diagram, evaluate the probability of passing the quiz, which the teacher defines as answering at least three questions correctly.