According to Broadcasting and Cable, Alex Trebek received a positive prognosis about his cancer treatment. The 78-year-old host of Jeopardy! was recently diagnosed with stage 4 pancreatic cancer. But his tumors are shrinking after a round of chemotherapy, which suggests his cancer is heading into remission. Trebek said the prognosis was mind-boggling, even to his doctors, because some of the tumors have shrunk to half their size.