Question: a terrible new virus has been discovered amongst beefcattle in...
A terrible new virus has been discovered amongst beef-cattle in Southern Alberta. It is estimated that 6% of all beef-cattle are infected with this virus. A team of veterinarians have developed a simple test. Indications are that this test will show a positive result - indicating the beef-cow being tested has the virus - with a probability of 0.95. Unfortunately, this test has a false-positive probability of 0.09.
(a) A beef-cow in Southern Alberta was randomly chosen and given this test. The test results were positive, indicating the beef-cow has the virus. What is the probability that this particular beef-cow actually does have the virus?
(b) What is the probability that a beef-cow that tests negative for this virus, actually has the virus?