Assume that you toss a fair coin 5 times. (a) What is the probability that you get 5 heads? (Show work and write the answer in simplest fraction form)(b) What is the probability of getting heads in the 5th toss, given that the first four tosses are tails? (Show work and write the answer in simplest fraction form)(c) If event A is “Getting heads in the 5th toss” and event B is “The first four tosses are tails”. Are event A and event B independent? Please explain. A high school with 1000 students offers two foreign language courses : French and Japanese. There are 150 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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