Probability with R, 2nd Edition

5Rules of Probability

So far, we have defined the issues relating to probability in an ad hoc way. Our approach to solving probability problems has been somewhat intuitive, treating each problem as it arrived as something new. We now formalize the definitions, and define the assumptions that we have made, or need to make, to develop the probability system further, by introducing the axioms of probability. We first provide some further notation on events.

5.1 Probability and Sets

In considering probability, it is enlightening to use the language and notation of sets.

If and are events in the sample space, then the union denotes the event “ or .”

Let us look at the simple experiment in Example 4.3 of pulling a card from a deck. Let be the event that we draw a spade and be the event that ...