Section 1.7 - Subsets of Sample Spaces

Given a predicate over a sample space,^?A predicate partitions the sample space into two subsets, one of which contains the outcomes that satisfy the predicate and the other of which contains the outcomes that don’t satisfy the predicate. what is the probability a trial will produce an outcome satisfying the predicate? That outcome probabilities add is an important fact to exploit when answering this question. Because outcome probabilities in a symmetric sample space are identical, the probability of a satisfactory outcome occurring is the sum of the probabilities of the satisfactory outcomes, or the ratio of the number of satisfactory outcomes overthe sample-space size. Handling complex predicates over large sample spaces is difficult and requires more math; just go for the main ideas now.

Probabilities are scaled to be in the range [0 (impossibility) .. 1 (certainty)], but other ranges are possible, such as [1 (certainty) .. \(\infty\) (impossibility)) or [0 (certainty) .. ∞ (impossibility)).^?The [1 .. \(\infty\)) range is the inverse of the [0..1] range. In either alternative range, combining outcome probabilities is a problem because simple addition doesn’t behave properly (combining to certainty, for example). Venn diagrams do not scale with the number of sample-space coordinates, and will not be considered further.