Probability ranking in differentials

A group of gastroenterologists is concerned about low colonoscopy screening rates. They decide to implement a free patient navigation program to assist local residents and encourage them to obtain colonoscopies in accordance with U.S. Preventive Services Task Force (USPSTF) guidelines. Local residents were recruited at community centers. Participants attended monthly meetings with patient navigators and were regularly reminded that their adherence to screening guidelines was being evaluated. Colonoscopy screening rates were assessed via chart review, which showed that 90% of participants adhered to screening guidelines. Data collected via chart review for local residents recruited at community centers who did not participate in the free patient navigation system found that 34% of that population adhered to USPSTF guidelines. Which of the following has most likely contributed to the observed disparity in colonoscopy screening rates?

A 14-month-old Caucasian boy is admitted to the pediatric clinic with an 8-month history of diarrhea, abdominal tenderness and concomitant failure to thrive. One of the possibilities that may cause these symptoms is Crohn’s disease, and on the basis of the attending pediatrician’s experience, the pre-test probability of this diagnosis was estimated at 40%. According to Fagan’s diagram (picture), if the likelihood ratio of a negative test result (LR-) is 0.04, what is the chance that this is the right diagnosis?