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Lecture2_print - STAT416 Probability Spring 2011 Lecture...

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STAT416: Probability — Spring 2011 Lecture Notes 1 Chapter 1: Sample Space, Equally Likely Sample Points, Combinatorics, Probability Calculations January 21, 2011 1 Introduction to Probability 1.2 Unions, Intersections, and Counting Problems Relations From Set Theory An event is a set of outcomes, we may use set theory to form new events . Union A B : is the event containing all outcomes in A or B . Intersection A B : is the event containing all outcomes in both A and B . Compliment A c : is the event containing all outcomes in the sample space S that are not contained in A . A A c = S Mutually Exclusive (Disjoint) : A and B are said to be mutually exclusive if they contain no outcome in common. A B = φ φ is the empty set. Disjoint Events Example 1 (Drawing Cards) . When drawing a single card from a standard deck of cards, if event A = { heart, diamond } ( red ) and event B = { spade, club } (black), then A and B are mutually exclusive. Example 2 (Rolling a Die) . When rolling a die, if event A = { 2 , 4 , 6 } (evens) and event B = { 1 , 3 , 5 } (odds), then A and B are mutually exclusive. Venn Diagram Venn diagram is a visual representation of events and their operations .
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