2. (5 points) Many pregnant people choose to have a screening test during the first trimester of their pregnancy to identify the probability of having an infant with down syndrome. Suppose the following are true: . 1% of infants have down syndrome. (Note: This is actually much higher than in reality.) . 2% of infants with down syndrome will be incorrectly identified as having no down syn- drome. (False negative rate) . 3% of infants without down syndrome will be incorrectly identified as having down syn- drome. (False positive rate) Answer the following question: "If the screening test is positive, what is the probability the infant does not have down syndrome?" You can answer the question by either completing the hypothetical two-way table below, or by using probability rules. (Hint: Bayes' Rule) Screening Test Positive test Negative test Total Infant has down syndrome No Colunm Total 10,060 hpPage of 6 3. Currently South Dakota and North Dakota are having the worst COVID outbreaks in the entire country. For example, according to the Georgia Tech COVID risk assessment tool, 15% of all residents in Stutzman County, ND currently have COVID. Use probability rules, including the binomial formula, and your calculator to answer the following questions. Do NOT use Statcrunch for this question. Include all probability notation. (a) (5 points) What is the probability that in a group of 10 randomly selected residents in Stutzman County, exactly 4 of them have COVID