PHL246H1 Lecture : Homework assignments 5 and 6(3).pdf
Document Summary
A probability space is a triple (w, a, pr) consisting of an arbitrary non-empty set of worlds or possibilities. W, an algebra a of propositions over w, and a probability measure pr: a . A probability measure pr: a is a function from the algebra of propositions a into the real numbers. Such that for all b and c in a: (1) pr(b) 0. (2) pr(w) = 1. (3) pr(b c) = pr(b) + pr(c) if b c = . If pr(c) > 0, the conditional probability of b given c, pr(b|c), is defined as pr(b c)/pr(c). If pr(c) = 0, the conditional probability of b given c, pr(b|c), is not defined. Show that the following claims hold true in a probability space (w, a, pr). Claim i: for all b in a, pr(b) = pr(b|w). (1 point) Claim ii: for all b in a, pr(b|b) = 1 if pr(b) > 0. (1 point)
