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The sample space associated with an experiment is the set of all possible outcomes (i.e., the set of all possible things that can happen) of the experiment. In an experiment, an event E is a subset of the sample space of the experiment. An event E is said to occur if the outcome of an experiment corresponds to one of the elements of E. 1. An urn is a vase whose contents are not readily visible. Your urn contains three blue marbles and two orange marbles. One marble is randomly selected, its color noted and it is not replaced. A second marble is then selected and its color noted. a. Draw a tree diagram and list the sample space showing all possible outcomes. b. What is the probability that . both marbles selected are orange? Justify your answer. neither marble selected is orange? Justify your answer. at least one of the marbles selected is orange? Justify your answer. at most one of the marbles selected is orange? Justify your answer. c. How would the probabilities in b. differ, if at all, if an actual experiment was conducted and you determined the probabilities based on the data from your experiment?CHAPTER 5 | 161 Activity 5.11: Basic Probability Notions 2. Jamaica is a first-year college student who is only beginning to organize her laun- dry. Specifically, she is still throwing her socks into the drawer without pairing them. One morning when Jamaica overslept, she hurriedly grabbed two socks from the drawer without looking. Jamaica knows that she has in her sock drawer 4 white socks, 2 blue socks, 2 black socks, and 2 tan socks. . If Jamaica first pulls out a tan sock, what is the probability that she will select another tan sock on the next try? Explain your reasoning. b. If Jamaica first pulls out a tan sock, what is the probability that she will not select another tan sock? Explain your reasoning. c. What are her chances of pulling out either a white sock or a blue sock on the first selection? Explain your reasoning. too! orli oun bangs d. What are the chances that Jamaica pulls out a pair of matching socks if she makes two selections? Explain your reasoning