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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
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
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
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
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
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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.
- Spring '08