Unformatted text preview: A is 1 / 36 times the number of elements in A . In both these cases, we assume that each number on each die is equally likely. We might have a “loaded” die, where P ( { 1 } ) = . 10, P ( { 2 } ) = . 15, etc. We do want something to happen, so P (Ω) = 1 and P ( ∅ ) = 0. The collection of events have to be what is called a σﬁeld. A collection F subsets of Ω is a σﬁeld if Ω , ∅ ∈ F , A c ∈ F whenever A ∈ F , and ∪ ∞ i =1 A i and ∩ ∞ i =1 A i are in F whenever all the A i are in F . A probability is a function on the events such that (1) 0 ≤ P ( A ) ≤ 1 for each event A . (2) P (Ω) = 1 and P ( ∅ ) = 0. (3) If A and B are disjoint, which means A ∩ B = ∅ , then P ( A ∪ B ) = P ( A ) + P ( B ) . 1...
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 Spring '10
 ansan
 Sets, Probability

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