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# ch14 - STAT 2023 Holbrook From Randomness to Probability 1...

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Unformatted text preview: STAT 2023 - Holbrook From Randomness to Probability Chapter 14 14 - 1 Trials & Outcomes STAT 2023 - Holbrook 1. Trial Process of obtaining an outcome. 2. Outcome The individual possibility that occurs on The each trial. each 3. Event Specific collection of outcomes. 4. Sample Space (S) 14 - 2 Collection of all possible outcomes. Collection all Outcome Examples STAT 2023 - Holbrook Trial Sample Space Toss a Coin, Note Face Toss 2 Coins, Note Faces Select 1 Card, Note Kind Select Select 1 Card, Note Color Play a Football Game Play Inspect a Part, Note Quality Observe Gender Head, Tail HH, HT, TH, TT 2♥, 2♦, ..., A♠ (52) Red, Black Red, Win, Lose, Tie Defective, OK Male, Female 14 - 3 Event Examples STAT 2023 - Holbrook Trial: Toss 2 Coins. Note Faces. Event Sample Space 1 Head & 1 Tail Heads on 1st Coin At Least 1 Head Heads on Both 14 - 4 Outcomes in Event HH, HT, TH, TT HT, TH HH, HT HH, HT, TH HH STAT 2023 - Holbrook Probabilities 14 - 5 What is Probability? STAT 2023 - Holbrook 1. Numerical measure of 1. likelihood that an outcome or event will occur. or P(A) 2. Lies Between 0 & 1 2. Lies 1 Certain .5 .5 3. Sum of Probabilities is 1 3. Sum 0 14 - 6 Impossible STAT 2023 - Holbrook Assigning Event Probabilities 1. a priori Classical 1. priori Method. Method. 2. Relative Frequency Relative Method. Method. 3. Personal Personal Probability Method. Probability 14 - 7 What’s the What’s probability? probability? a priori Classical Method STAT 2023 - Holbrook 1. Prior Knowledge of the 1. Process. Process. 2. Before Experiment 3. P(Event) = X / T (Event) 14 - 8 X = No. of Event Outcomes T = Total Outcomes in Sample Space Each of T Outcomes Is Equally Likely P(Outcome) = 1/T © 1984-1994 T/Maker Co. STAT 2023 - Holbrook Relative Frequency Method 1. Actual Data Collected 2. Probability is determined 2. after the trial. 3. P(Event) = X / T (Event) Repeat the trial Repeat T Times Event Observed X Times Event 14 - 9 Of 100 Parts Of Inspected, Only 2 Defects! Defects! Law of Large Numbers STAT 2023 - Holbrook • • Long-run relative frequencies of Long-run repeated independent trials get closer and closer to the TRUE relative frequency as the number of trials increases. increases. Allows us to use the relative frequency Allows method with assurance. method 14 - 10 10 STAT 2023 - Holbrook Personal Probability Method 1. Also called the Subjective Method. 2. Probabilities obtained by personal Probabilities assessment and experience. assessment 3. Probabilities are NOT based on relative Probabilities frequencies or a priori probabilities. priori 14 - 11 11 STAT 2023 - Holbrook Addition Rule for Disjoint Events 1. For Disjoint Events • Events that do not occur simultaneously 2. P(A OR B) = P(A ∪ B) = P(A) + P(B) 2. OR P(A 14 - 12 12 STAT 2023 - Holbrook Multiplication Rule for Independent Events 1. For Independent Events • Independence defined in Chapter 15. 2. P(A AND B) = P(A ∩ B) = P(A)*P(B) 2. AND 14 - 13 13 Statistical Independence STAT 2023 - Holbrook 1. Event Occurrence Event Does Not Affect Probability Not of Another Event of 2. 2. 14 - 14 14 Toss 1 Coin Twice Finding a red light today Finding and finding a red light tomorrow Causality Not Implied Complement Rule STAT 2023 - Holbrook 1. Complement of Event For Event A, All Events Not In A: AC 2. Example: Let A be the event that you pass this class and P(A)=0.80 What is the the probability of NOT passing this class; or what is P(AC)? class; 3. P(AC) = 1 – P(A) also, P(A) = 1 – P(AC) 14 - 15 15 End of Chapter Any blank slides that follow are blank intentionally. ...
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