Denition 244 events a b and c are pairwise

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Unformatted text preview: is just a single equation that can be true even if A and B are not physically independent. Example 2.4.2 Consider a probability experiment related to the experiment discussed in Section 1.3, in which a fair coin is flipped and a die is rolled, with N denoting the side showing on the coin and X denoting the number showing on the die. We should expect the event {N = H } to be independent of the event {X = 6}, because they are physically independent events. This independence holds, assuming all twelve outcomes in Ω are equally likely, because then P {N = H } = 6/12, P {X = 6} = 2/12, and P {N = H, X = 6} = 1/12, so P {N = H, X = 6} = P {N = H }P {X = 6}. More generally, any event involving only X is independent of any event involving only N. Example 2.4.3 Suppose the probability experiment is to roll a single die. Let A be the event that the outcome is even, and let B be the event that the outcome is a multiple of three. Since these events both involve the outcome of a single role of a die, we...
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