Chapter 12

# Chapter 12 - STAT 2053 Elementary Statistics Chapter 12...

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STAT 2053 – Elementary Statistics Chapter 12 – General Rules of Probability

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Chapter 12 2 Probability Rules from Chapter 10 Chapter 12 focuses on some other rules of probability that we didn’t cover in Chapter 10. To recap:
Venn Diagrams Definition : For a random phenomenon, a Venn diagram is a picture that shows the sample space as a rectangle. Events are depicted as areas within the rectangle. Example : For sample space S and event A: 3 S A Chapter 12

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Chapter 12 4 Venn Diagrams Two disjoint events: Two events that are not disjoint, and the event {A and B} consisting of the outcomes they have in common:
Venn Diagrams Venn diagrams are helpful tools to display how several different events are related. Example : Draw a Venn diagram for two events (A and B) that are disjoint. 5 Chapter 12

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Venn Diagrams Example : Draw a Venn diagram with two events (A and B) that are not disjoint. 6 Chapter 12
Independent Events Definition : Two events are said to be independent if knowing that one occurred does not change the probability of the other occurring. Example : Suppose I flip two coins. Does knowing the result of the first flip change the probability of getting a head on the second flip? 7 Chapter 12

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Independent Events Fact : If two events are independent , the probability that they both happen is found by multiplying their individual probabilities: If A and B are independent events, then 8 Chapter 12 P(A and B) = P(A) × P(B)
Chapter 12 9 Multiplication Rule for Independent Events Example Suppose that about 20% of incoming male freshmen smoke. Suppose these freshmen are randomly assigned in pairs to dorm rooms (assignments are independent ). The probability of a match ( both smokers or both non-smokers ): both are smokers: 0.04 = (0.20)(0.20) neither is a smoker: 0.64 = (0.80)(0.80) only one is a smoker: ? } 68% 32% (100% - 68%)

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Multiplication Rule Example : If A = Getting a head on the 1 st coin, and B = Getting a head on the 2 nd coin, what’s the probability of getting heads on both coins? Chapter 12 10
Independent Events Example : Suppose that I roll two dice, and the results of each dice roll are independent. What’s the probability of rolling a 1 on both dice? 11 Chapter 12

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Independent Events Something to ponder: Are the two cards you are dealt at the beginning of a Blackjack hand independent? i.e. Does knowing what you got for one card tell you anything about the value of the other card? 12
Example : Let’s draw two cards from a 52 card deck. There are 26 red cards and 26 black cards. If the first card I draw is a red card, what

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## This note was uploaded on 09/23/2011 for the course STAT 2053 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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Chapter 12 - STAT 2053 Elementary Statistics Chapter 12...

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