A test that is wrong 50% of the time can be replaced with a coin toss.


Not true actually, a test with a 50% chance of being wrong can be quite useful.

Suppose 2% of the population has the disease. Take a test that has 100% chance of positive if you do have it, and 50% chance of positive if you don't have it. It tells the 2 people who do have it they have it, and it tells one other healthy person he has it too. Three people stay home, 97 go soaring in perfect safety.

Take a test that has 100% chance of negative if you don't have it, but 50% chance of positive if you do have it. 98 people are correctly cleared, 1 person is incorrectly cleared, 1 stays home. Well, we got half the sick people out of the population and reduced the reproduction rate by half.

John Cochrane.