Lecture2

# Let b be the event that the rst 2 tosses are tails

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Unformatted text preview: Let B be the event that the ﬁrst 2 tosses are tails. Let C be the event that all 3 tosses are tails. What are A ∩ B , A ∪ C , and (A ∩ B ) ∪ C ? Solution. Venn Diagrams; Probability Laws Set Operations and Relations Venn Diagram 2.4 Notes Logical Relationships among Sets Mutually exclusive: refers to two (or more) events that cannot both occur when the random experiment is formed. A∩B =∅ Venn Diagrams; Probability Laws Notes Set Operations and Relations Venn Diagram Exhaustive: refers to event(s) that comprise the sample space. A∪B =Ω Partition: events that are both mutually exclusive and exhaustive. A∩B =∅ and A ∪ B = Ω 2.5 Venn Diagrams; Probability Laws Complement Rule The complement rule is a way to calculate a probability based on the probability of its complement. 1 By the deﬁnition of complement A ∪ Ac = Ω Set Operations and Relations Venn Diagram 2 Apply the probability operator P(A ∪ Ac ) = P(Ω) = 1 3 Since A and Ac are mutually exclusive P(A ∪ Ac ) = P(A) + P(Ac )...
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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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