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1. Assume that you make random guesses for 5 true-or-false questions.
(a) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form)
(b) What is the probability of getting the correct answer in the 5th question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form)
(c) If event A is "Getting the correct answer in the 5th question" and event B is "The first four answers are all wrong". Are event A and event B independent? Please explain.
2. A high school with 1000 students offers two foreign language courses: French and Japanese. There are 200 students in the French class roster, and 80 students in the Japanese class roster. We also know that 30 students enroll in both courses. Find the probability that a random selected student takes neither foreign language course. (Show work and write the answer in simplest fraction form)
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