Standard view of scientific inference has a set of theories which make predictions about the outcomes of an experiment:
| Theory | Prediction |
| A | 1 |
| B | 2 |
| C | 3 |
Conduct experiment, see outcome 2: infer B is correct (or at least A and C are wrong).
Add Randomness
| Theory | Prediction |
| A | Usually 1 sometimes 2 never 3 |
| B | Usually 2 sometimes 1 never 3 |
| C | Usually 3 sometimes 1 never 2 |
See outcome 2: infer Theory B probably correct, Theory A probably not correct, Theory C is wrong.
Probability Theory: construct table: compute likely outcomes of experiments.
Statistics: inverse process. Use table to draw inferences from outcome of experiment. How should we do it and how wrong are our inferences likely to be? Notice: hopeless task unless different theories make different predictions.
Start with Probability; switch after about 5 weeks to statistics.