Section2.3-students_SP11

Section2.3-students_SP11 - Recap Axioms and Properties of...

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1 Recap… Axioms and Properties of Probability Axiom: A1) P( S ) = 1 A2) P( E ) 0 for every event E S A3) For mutually exclusive events, Properties: 1) P( ) = 0 2) 3) 4) Today: Simple Rules for counting the number of “simple” outcomes in an event 1. Counting the Number of Operations - Product Rule (Page 60-61) If an operation consists of k steps, and there are n 1 choices for the first step, . .., n k choices for the k th step, then the total number of operations possible is the product n 1 × n 2 × × n k Logic: Use Tree Diagram 2. Basic Problem: Select a subgroup of size k from n objects. How many possible ways? Answer depends on “rules”: 1. Order: Matters (permutation) or doesn’t matter (Combination) 2. Replacement: Yes or No. So four types of situations 2 Section 2.3
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2 Counting Techniques Useful for Probability Calculations Focus: Situation where S is finite and has N outcomes, and all N simple events are equally likely. Let A be an event, and N(A) be the number of outcomes in A : 3 Section 2.3 For a small sample space, you can enumerate all outcomes and then count manually. Example: Roll two dice and sum them: N ( S ) = 36 simple events Not always easy to enumerate manually. 4 Section 2.3
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3 Product rule for k -tuples A k -tuple is an ordered collection of k elements: ... n 2 distinct objects of doing Task 2 n k distinct objects of doing Task k ( , , ... , ) How many different k -tuples can be made this way? 5 Section 2.3 n 1 distinct ways of doing Task 1 Product rule for k -tuples 6 Section 2.3 ... n
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Section2.3-students_SP11 - Recap Axioms and Properties of...

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