Slides Week 2

# Slides Week 2 - (SECTION1.4ANDCHAPTERS2,3,AND4)

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(SECTION 1.4 AND CHAPTERS 2, 3, AND 4)

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We will be covering Chapter 2 slightly out of order. We will cover 1.4, then 2.2 and 2.3, and finally we will cover sections 2.1 and 2.4.
DEFN: A  Universal Set Universal Set  is  the largest set that needs   to be considered for a given selection problem. RECALL FROM LAST WEEK….

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SELECTION EXPERIMENTS: DEFN:  A  Selection Experiment (or problem) Selection Experiment (or problem)  is any  process that involves selecting objects (elements) from sets. DEFN:  An  Outcome Outcome  to a selection experiment is a list of  everything everything that was selected during the  experiment, along with any labels needed to specify the roles the selected objects are playing. DEFN:  The  Sample Space (S) Sample Space (S)  of a selection experiment is the set of all possible outcomes to the experiment (ie, the  UNIVERSAL SET  for the selection experiment).
A very simple Selection Experiment A very simple Selection Experiment :  I roll a 6-sided die  once and note which number lands up. Q:  What does S contain for this experiment?

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A simple Selection Experiment A simple Selection Experiment :  I roll a 6-sided die once and note which number lands up. Q:  What does S contain for this experiment? The  SOS SOS  (Selecting Objects from Sets) model: 1 2 6 3 5 4 The Set & Objects The Selection Process “Select” one object from set, note # on face
Outcome (option) Trees and Sample Spaces: START 1 2 3 4 5 6 { 1,   2,   3,   4,   5,   6 } = S S = {1, 2, 3, 4, 5, 6 } n(S) = 6 1 2 6 3 5 4

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THE SETUP: THE SETUP:   A box contains three ferrets, numbered 1, 2, and 3.   EXPERIMENT #1 EXPERIMENT #1 : An experiment consists of selecting two ferrets from the box, one after another and  WITH replacement, and noting the number on each ferret.  Find S and n(S). EXPERIMENT #2 EXPERIMENT #2 : An experiment begins by selecting a ferret from the box and noting its number.  If the  selected ferret’s number is “3”, the ferret is replaced and one more ferret is then selected from the box, noting its  number. However, if the 1 st  selected ferret’s number is not “3”, it is set free, and then one more ferret is  selected from the box, noting its number.  Find S and n(S). EXPERIMENT #3 EXPERIMENT #3 :   An experiment consists of selecting three ferrets from the box, one after another and  WITHOUT replacement, and noting the number on each ferret.  Find S and n(S). EXPERIMENT #4 EXPERIMENT #4 : An experiment consists of selecting ferrets from the box, one after another and without  replacement, until the number “2” ferret is selected, at which time the experiment stops.  Find S and n(S).
THE MULTIPLICATION PRINCIPLE: THE MULTIPLICATION PRINCIPLE:

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## This note was uploaded on 11/16/2010 for the course MATH 118 taught by Professor Stevemckinley during the Spring '10 term at Indiana.

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Slides Week 2 - (SECTION1.4ANDCHAPTERS2,3,AND4)

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