What are the odds of two unrelated women, living in the same household developing ulcerative colitis?

Hard to say. The annual incidence of ulcerative colitis (uc) varies from place to place in the world. Studies report the annual incidence to be anywhere from 0.5 cases per 100, 000 people to 25 per 100, 000 people. Since uc has been linked to certain diets, meds, environmental exposures, etc., it would make sense that two women living together would be exposed to similar risk factors. Short answer: low odds.