MAT 2377 Lecture Notes - Lecture 2: Electronic Component, Mutual Exclusivity, Beijing Capital International Airport
9 May 2014
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De nition: if p (b) > 0, the conditional probability that a will occur given that b occurs is. Remark: we can show that the function p ( |b) satis es the three probability axioms. Thus, the consequences of the axioms also apply to condition probabilities. For the latter approach, we interpret p (a|b) as the proportion of out- comes from b that satisfy criteria for a. Remark: we can also interpret the context for which we use a condi- tional probability as a change in the experimental conditions. Example 3: consider a box of 20 light bulbs where in 2 bulbs are defective. P (a b) = p (b | a)p (a) = p (a | b)p (b) Example 4: consider a box of 20 light bulbs where in 2 bulbs are defective. Suppose that we choose two bulbs without replacement. P (b) = p (a b) + p (a(cid:48) b)
