8. There are 8 books in the “Statistics is Fun” series. (Show all work. Just the answer, without supporting work, will receive no credit). (a) How many different ways can Mimi arrange the 8 books in her book shelf? (b) Mimi plans on bringing two of the eight books with her in a road trip. How many different ways can the two books be selected?
7. Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be the event that the first one lands on 6.
(a) What is the probability that the first one lands on 6 given that the sum of the two dice is 8? Show all work. Just the answer, without supporting work, will receive no credit. (b) Are event A and event B independent? Explain.
6. There are 1000 students in a high school. Among the 1000 students, 200 students take AP Statistics, and 300 students take AP French. 100 students take both AP courses. Let S be the event that a randomly selected student takes AP Statistics, and F be the event that a randomly selected student takes AP French. Show all work. Just the answer, without supporting work, will receive no credit.
(a) Provide a written description of the complement event of (S OR F). (b) What is the probability of complement event of (S OR F)?
10. Mimi plans on growing tomatoes in her garden. She has 15 cherry tomato seeds. Based on her experience, the probability of a seed turning into a seedling is 0.40.
(a) Let X be the number of seedlings that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? (b) Find the probability that she gets at least 2 cherry tomato seedlings. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit
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