Explain that there are three equivalent sets of probabilities:
- The joint probabilities, pxy
- The marginal probabilities for X, px,
and the conditional probabilities for Y, py | x
- The marginal probabilities for Y, py,
and the conditional probabilities for X, px | y
The formulae for moving between the 2nd and 3rd of these is called Bayes theorem.
- Click on joint probabilities to see how they are related to the initial (green)
information.
- Click on any of the black marginal probabilities to see how they are obtained
from the joint probabilities.
- Click on the conditional probabilities on the bottom right to see how they
are found from the joint and marginal probabilities.
Medical diagnostic tests for a disease are rarely 100% accurate. There are
two types of error:
- A positive test result for someone who does not have the disease.
- A negative test result for someone who has the disease.
The probabilities are not for a real disease or diagnostic test.