Use Bayes' Theorem to solve the following problem. (20 pts.) It's well known that Franklin Delano Roosevelt (FDR) was stricken with a paralytic illness in 1921, when he was 39 years old. At the time he was diagnosed with poliomyelitis, commonly known as polio. A 2003 study challenged this diagnosis, proposing that FDR actually had Guillain-Barre syndrome (GBS). Previous studies indicated that among FDR's age group, 51% of paralytic illnesses were due to GBS and 49% were due to polio. Researchers noted that FDR experienced bladder dysfunction for two weeks following the initial onset of his illness. This symptom occurs in very few cases of polio-5 in every 100 cases-but in 50% of GBS cases. Given this evidence, how likely are each of the competing diagnoses? (20 pts.)