In the state of Texas 58% of the population is vaccinated. Assume that 80% of people that are vaccinated do not get COVID-19. People that are not vaccinated are 3 times more likely to get COVID-19. a.) Draw and completely fill out the tree diagram representing the probabilities in this problem. b.) What is the probability of being vaccinated if you have tested positive? c.) If the rate of vaccination in Texas went up to 80%, what would be the probability of being vaccinated if you have tested positive? d.) A breakthrough infection is when you are vaccinated but still contract COVID. As more people are getting vaccinated, we are observing more breakthrough infections. Compare your results from parts (b) and (c). When the vaccination rates increase, is there a higher, lower, or same probability of being vaccinated if you have tested positive? Using Bayes Theorem, interpret this finding (specifically interpret the numerator and denominator in Bayes Theorem). As part of your solution, create a table that has different values of the probability of vaccination along with the associated numerator and denominator in the Bayes equation, as well as the associated probability of being vaccinated given a positive test