4) A study published in March of 2021 found that COVID-19 antigen tests correctly identified COVID-19 infections in 72% of people with symptoms, compared to 58% of people without symptoms (Dinnes et al. 2021). The tree diagram below shows the possible outcomes with the associated probabilities. Out of all COVID-19 positive individuals, only 41% of individuals are symptomatic (Ma et al. 2021). What is the probability of getting an incorrect test result from an antigen test when you have COVID-19? Give your answer as a decimal precise to two decimal places. COVID-19 Test Result Status for individuals who have the virus 0.72 Positive Sympto- matic 0.41 0.28 Negative Positive 0.58 0.59 Asympto -matic 0.42 Negative 5) Consider the following: In a population of 2 species of trees, 45% of trees are elms and the other 55% of trees are oaks. If 60% of the trees are infected with a disease, which of the following statements is/are correct? Assume that the infection is independent from the tree species. [Choose all correct answers] The probability of randomly selecting an elm tree is 0.45. The probability of randomly selecting an infected tree or an elm tree is 0.78. The probability of randomly selecting an infected tree or an elm tree is 1. The probability of randomly selecting either an oak or elm tree is 1. 6) State whether the following statement is True or False, and explain why or why not: "The addition rule states that Pr[A and B] = Pr[A] + Pr[B]."1) If A and B are mutually exclusive events and Pr[A] = 0.3 and Pr[B] = 0.2, then what is Pr[A and B]? 0 0.06 0.5 0.6 2) When whether one event happens or not provides no information about whether a second event happens or not, we say the two events are _?_ Dependent Independent Mutually exclusive Probabilistically distinct 3) Suppose a researcher conducted four separate experiments. Match the appropriate figure from the figures labeled A-D with each of the following descriptions (1 pt. each): Loaded Die: A loaded die is rolled several thousand times. This die is known to produce larger values more often than it produces small values: Figure A Urn: Three hundred balls are placed into an urn. Of the 300 balls, 200 are black and 100 are white. A total of 6 balls are drawn from the urn, the number of black balls is recorded, and the balls are placed back into the urn. This process is repeated several thousand times. Figure A B C D A 3000 B 3000 2000- 2000- Count Count 1000 2 2 3 Value Value C 1000 D 2000 750 1500- Count Count 500 1000 250- 500- 2 3 12 Value Value 4) A study published in March of 2021 found that COVID-19 antigen tests correctly identified COVID-19 infections in 72% of people with symptoms, compared to 58% of people without symptoms (Dinnes et al. 2021). The tree diagram below shows the possible outcomes with the associated probabilities. Cutor viviquans, only 41% of individuals are38) In R, the dbinom() function is used to find the probability of a specific number of successes. What function is used to run a binomial test (that gives you your P-value for the test statistic)? binom() binomial() binom.test() binomial.test() 39) In R, the binomial test requires the same three pieces of information as the dbinom() function. What does x refer to? The proportion of successes The null proportion The number of successes The sample size Here is the output from the Binomial Test: Exact binomial test data: 12 and 31 number of successes = 12, number of trials = 31, p-value