3.3 The sample space for an experiment contains five sample NW points with probabilities as shown in the table. Find the probability of each of the following events: Sample Points Probabilities 05 20 .30 30 .15 A: { Either 1, 2, or 3 occurs. } B: { Either 1, 3, or 5 occurs.} C: {4 does not occur.} 3.4 Compute each of the following: a b. C. d. 6 e. 3.15 Unused paid vacation time. According to a 2019 Bankrate survey, most Americans do not use all of their PADpaid vacation days. The most likely reason cited was that vacations are too expensive. Consider the survey ques- tion: "How many of your paid vacation days do you plan to use (this year)?" The results are summarized in the accompanying table. Response Percentage All 38 Almost all 21 About half 17 About a quarter 7 Less than a quarter 5 None Unsure (because I have unlimited days) Source: "Survey: High costs are keeping many Americans from summer vacation", www.bankrate.com, April 25, 2019. a. What is the probability that a randomly selected American with paid vacation time will use all of their paid vacation days this year? b. What is the probability that a randomly selected American with paid vacation time will use at least half of their paid vacation days this year?3.42 Policies for Singlish. Singlish is a colloquial form of English used in Singapore that has been influenced by other lan- guages such as Chinese, Malay Mandarin, and Tamil. A study published in the International Journal of Academic Research in Progressive Education and Development (Vol. 9, 2020) investigates the use of Singlish by 82 adults in Singapore. It also analyzes the general perception of the adults towards Singlish. The study found that 82.9% of the participants did not agree that Singlish should be made an official language in Singapore, 3.7% said that it should be made an official language, while the remainder were unsure. Suppose 3.4% of the participants were neu- tral towards the idea and registered this by answering both "agree" and "disagree" a. Draw a Venn diagram to illustrate the participants' per- ceptions on whether Singlish should be made an official language in Singapore. b. Find the probability that a participant either agreed or disagreed with the argument that Singlish should be made an official language in Singapore. c. Use your answer to part b to find the probability that a participant answered neither "agree" nor "disagree" 3.48 Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on a problem was investi- gated in the Jan. 2007 issue of the Journal of Behavioral Decision Making (see Exercise 1.32, p. 47). A total of 171 volunteer students participated in the experiment, where each was randomly assigned to one of three emotional states (guilt, anger, or neutral) through a reading/writing task. Immediately after the task, students were presented with a decision problem where the stated option had pre- dominantly negative features (e.g., spending money on re- pairing a very old car). The results (number responding in each category) are summarized in the accompanying table. Suppose one of the 171 participants is selected at random. Choose Do Not Emotional Stated Choose State Option Stated Option Totals Guilt 45 12 57 Anger 50 58 Neutral 49 56 Totals 60 111 171 Source. Bailed on A. Gangemi and F. Mancini, "Guilt and Focusing in Decision-Making," Joumal of Behaviorl Dechion Making, Vel. 201, January. 2007 (Table !). a. Find the probability that the respondent is assigned to the guilty state. b. Find the probability that the respondent chooses the stated option (repair the car). c. Find the probability that the respondent is assigned to the guilty state and chooses the stated option. d. Find the probability that the respondent is assigned to the guilty state or chooses the stated option.Problem 7 [18pts, each 6pt] Suppose that in the packaged-cereals industry, 29% of all vice presidents hold MBA degrees, 24% hold undergraduate business degrees, and 8% hold both. A vice president is to be selected at random. (a) What is the probability that the vice president holds either an MBA or an undergraduate business degree (or both)? (b) What is the probability that the vice president holds neither degree? (c) What is the probability that the vice president holds an MBA degree but not an undergraduate business degree