Benja: Wrong analogy. You left out a bit. All people who actually HAVE CANCER AND that would get a POSITIVE RESULT are killed during the mammograph, never to receive the result. Your task is then to condition on first receiving a result and then that result being positive and alter your estimate of how likely you are to have cancer.
(Depending on how you meant the analogy it may be the negative result + positive actual cancer who are killed. Point is, your analogy completely misses the point. Not every person who takes the test gets a result but you do. That is important.)
Benja: Wrong analogy. You left out a bit. All people who actually HAVE CANCER AND that would get a POSITIVE RESULT are killed during the mammograph, never to receive the result. Your task is then to condition on first receiving a result and then that result being positive and alter your estimate of how likely you are to have cancer.
(Depending on how you meant the analogy it may be the negative result + positive actual cancer who are killed. Point is, your analogy completely misses the point. Not every person who takes the test gets a result but you do. That is important.)