Pa b c pa pb pc pa b pb c pa

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Unformatted text preview: 3 or more events. Here we will limit it to 3 events. P(A ∪ B ∪ C ) = P(A) + P(B ) + P(C ) − P(A ∩ B ) − P(B ∩ C ) − P(A ∩ C ) + P(A ∩ B ∩ C ) Venn Diagrams; Probability Laws Set Operations and Relations Venn Diagram 2.10 Notes Venn Diagrams; Probability Laws Law of Partitions Notes The law of partitions is a way to calculate the probability of an event. Let A1 , A2 , · · · , Ak form a partition of Ω. Then, for all events B , k P(Ai ∩ B ) P(B ) = i =1 Set Operations and Relations Venn Diagram 2.11 DeMorgan’s Law Venn Diagrams; Probability Laws Let A and B be subsets of Ω. Then (A ∩ B )c = Ac ∪ B c (A ∪ B )c = Ac ∩ B c Set Operations and Relations Venn Diagram 2.12 Notes Example 10 Three of the major commercial computer operating systems are Windows, Mac OS, and Red Hat Linux Enterprise. A Computer Science professor selects 50 of her students and asks which of these three operating systems they use. The results for the 50 students are summarized below. Venn Diagrams; Probability Laws Notes Set Operations and Relations Venn Diagram 30 students use Windows ⇒ #(W ) = 30 16 students use at least two of the operating systems ⇒ #(W ∩ M ∪ W ∩ L ∪ M ∩ L) = 16 9 students use all three operating systems ⇒ #(W ∩ M ∩ L) = 9 18 students use Mac OS ⇒ #(M ) = 18 46 s...
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This note was uploaded on 01/24/2014 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue.

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