In this lesson, we learn the fundamental concepts of probability. It is this lesson that will allow us to start putting our first tools into our new probability toolbox.
Upon completion of this lesson, you should be able to:
- Learn why an understanding of probability is so critically important to the advancement of most kinds of scientific research.
- Learn the definition of an event.
- Learn how to derive new events by taking subsets, unions, intersections, and/or complements of already existing events.
- Learn the definitions of specific kinds of events, namely empty events, mutually exclusive (or disjoint) events, and exhaustive events.
- Learn the formal definition of probability.
- Learn three ways — the person opinion approach, the relative frequency approach, and the classical approach — of assigning a probability to an event.
- Learn five fundamental theorems, which when applied, allow us to determine probabilities of various events.
- Get lots of practice calculating probabilities of various events.