Chapter4_IntroductionProbability

# Chapter4_IntroductionProbability - Chapter 4 Introduction...

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Chapter 4 Introduction to Probability

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Probability Concepts We will discuss the role probability plays in making inferences about a population based on a sample What is your definition of (or thoughts about) probability? We deal with probability in many aspects of our lives: Investing money Business decisions Gambling
Gambling… the Classic Example Gambler interested in determining if a die is balanced Using the scientific method, the gambler proposes that the die is fair. To test hypothesis, rolls die 10 times The result is 10 1’s Gambler concludes that die is not balanced

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Probability Concepts (cont) Experiment Process that leads to a single outcome that cannot be predicted with certainty Examples: Coin and/or die tossing Vehicle crash tests Test marketing products When an experiment is performed, it can result in one or more outcomes, called events .
Probability Concepts (cont) Simple Event An event or outcome that cannot be decomposed into simpler outcomes. – Denoted by E i Example: Toss a balanced die Simple events: 1, 2, 3, 4, 5, 6 If the event is that we observe an odd number Outcomes decomposed as 1, 3, 5

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Probability Concepts (cont) Sample Space (S) The collection of all simple events Example: Observe the face on a die Sample space: S = {1, 2, 3, 4, 5, 6} Venn Diagram 6 1 5 4 2 3 S
Probability Concepts Set Theory Let’s consider two sets, A and B. A B S

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Probability Concepts Set Theory Union A B S
Probability Concepts Set Theory Intersection A B S

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Probability Concepts Set Theory Complement S Ac
Probability Concepts Set Theory Mutually Exclusive

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Probability Concepts Set Theory - Example Consider the die-tossing problem S={1,2,3,4,5,6} Let A={1,2}; B={1,3}; and C={2,4,6} Determine the following: A B A B A c A C B C
Probability Concepts Determining Probability of Simple Event When assigning probabilities, we must have the following properties:

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Probability Concepts Sample Point Method 1. Define the experiment 2. List the simple events associated with the experiment and test each to make certain that they cannot be decomposed. 3. Assign probabilities to the simple events (make sure that the prob. 0 and that they sum to 1) 4. Define the event of interest and make sure that the simple events are contained in the events of interest 5. Sum the probability of the simple events to obtain the event probability
Sample Point Method Example 1 Consider tossing a balanced coin three times. Calculate the probability of exactly two of the three tosses turn out to be heads

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Sample Point Method Example 2 Consider a situation where cars entering an intersection each could turn L, R, or go S. An experiment. consists of observing 2 vehicles moving through the intersection. What is the probability that at least one car turns left.
Probability Concepts Counting Techniques

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Chapter4_IntroductionProbability - Chapter 4 Introduction...

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