Jennifer decided to have a barbecue. She invited John over and offered him a piece of wild boar. Unfortunately, the boar was not cooked all the way through, and John became worried that he may have...

Jennifer decided to have a barbecue. She invited John over and offered him a piece of wild boar. Unfortunately, the boar was not cooked all the way through, and John became worried that he may have contracted a disease which is known to be transmitted by exposure to raw boars. Having talked to an expert on infectious diseases, John believes that he has a 1 in 50 chance of having the disease. John is a bit worried and goes to his doctor to take a test known to be 90% accurate in predicting this disease. In the doctor's office, John finds out that the test came back positive. Given his other beliefs, with what probability does John believe the (positive) test report is correct?