Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula. 13. Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions. a. Use the multiplication rule to find the probability that the first two guesses are wrong and the third is correct. That is, find P(WWC), where W denotes a wrong answer and C denotes a correct answer. b. Beginning with WWC, make a complete list of the different possible arrangements of two wrong answers and one correct answer, then find the probability for each entry in the list. c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made? 14. News Source Based on data from a Harris Interactive survey, 40% of adults say that they prefer to get their news online. Four adults are randomly selected. continueda. Use the multiplication rule to find the probability that the first three prefer to get their news online and the fourth prefers a different source. That is, find P(OOOD), where O denotes a preference for online news and D denotes a preference for a news source different from online. b. Beginning with OOOD, make a complete list of the different possible arrangements of those four letters, then find the probability for each entry in the list. c. Based on the preceding results, what is the probability of getting exactly three adults who prefer to get their news online and one adult who prefers a different news source. SAT Test. In Exercises 15-20, assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n = 8 trials, each with probability of success (correct) given by p = 0.20. Find the indicated probability for the number of correct answers. 15. Find the probability that the number x of correct answers is exactly 7. 16. Find the probability that the number x of correct answers is at least 4. 17. Find the probability that the number x of correct answers is fewer than 3. 18. Find the probability that the number x of correct answers is no more than 2. 19. Find the probability of no correct answers. 20. Find the probability that at least one answer is correct.Ultimate Binomial Exercises! Exercises 37-40 involve finding binomial probabilities, finding parameters, and determining whether values are significantly high or low by using the range rule of thumb and probabilities. 37. M&Ms Data Set 27 "M&M Weights" in Appendix B includes data from 100 M&M candies, and 19 of them are green. Mars, Inc. claims that 16% of its plain M&M candies are green. For the following, assume that the claim of 16% is true, and assume that a sample consists of 100 M&Ms. a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the result of 19 green M&Ms significantly high? b. Find the probability of exactly 19 green M&Ms. c. Find the probability of 19 or more green M&Ms. d. Which probability is relevant for determining whether the result of 19 green M&Ms is sig- nificantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 19 green M&Ms significantly high? e. What do the results suggest about the 16% claim by Mars, Inc.? 38. Politics The County Clerk in Essex, New Jersey, was accused of cheating by not using ran- domness in assigning line positions on voting ballots. Among 41 different ballots, Democrats were assigned the top line 40 times. Assume that Democrats and Republicans are assigned the top line using a method of random selection so that they are equally likely to get that top line. a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the result of 40 top lines for Democrats significantly high? b. Find the probability of exactly 40 top lines for Democrats.c. Find the probability of 40 or more top lines for Democrats. d. Which probability is relevant for determining whether 40 top lines for Democrats is signifi- cantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 40 top lines for Democrats significantly high? e. What do the results suggest about how the clerk met the requirement of assigning the line positions using a random method