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# A BOX CONTAINS 3 MARBLES, 1 RED, 1 GREEN, AND 1 BLUE. CONSIDER AN EXPERIMENT THAT CONSISTS

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STAT 200: Introduction to StatisticsFinal Examination, Spring 2016 OL4Page 1 of 45.A box contains 3 marbles, 1 red, 1 green, and 1 blue. Consider an experiment that consists oftaking 1 marble from the box, then replacing it in the box and drawing a second marble fromthe box. (Show all work. Just the answer, without supporting work, will receive no credit.)(a)(b)List all outcomes in the sample space.What is the probability that neither marble is red?fraction form)6.There are 1000 students in a high school. Among the 1000 students, 250 students take APStatistics, and 300 students take AP French. 100 students take both AP courses. Let S be theevent that a randomly selected student takes AP Statistics, and F be the event that a randomlyselected student takes AP French. Show all work. Just the answer, without supporting work,will receive no credit.(a)(b)Provide a written description of the complement event of (S OR F).7.Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be theevent 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.Are event A and event B independent? Explain.(Express the answer in simplestWhat is the probability of complement event of (S OR F)?(b)9.Assume random variable x follows a probability distribution shown in the table below.Determine the mean and standard deviation of x. Show all work. Just the answer, withoutsupporting work, will receive no credit.xP(x)-20.100.210.330.150.310.Mimi plans on growing tomatoes in her garden. She has 15 cherry tomato seeds. Based on herexperience, 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 abinomial probability distribution. What is the number of trials (n), probability of successes (p)and probability of failures (q), respectively?STAT 200: Introduction to StatisticsFinal Examination, Spring 2016 OL4Page 2 of 4(b)

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