In a certain population of people 5% have a disease. Bob’s road side clinic use a test for the disease which has a 97% of (correctly) returning positive if one has the disease and a 25% chance of (incorrectly) returning a positive if one doesn’t have the disease. If a random person is given the test, what is the chance that the result is positive ?
Now let \(\alpha\) be the chance the test returns a positive if one doesn’t have the disease. (Leave the chance that the test correctly returns a positive is one has the disease at 97%). For what value of \(\alpha\) is the chance the test is correct equal to 5% for a randomly chosen person ?