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STP 231

by: Goran Notetaker

STP 231 STP 231

Goran Notetaker

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stp 231
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This 4 page Bundle was uploaded by Goran Notetaker on Wednesday October 28, 2015. The Bundle belongs to STP 231 at Arizona State University taught by in Fall 2015. Since its upload, it has received 44 views.


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Date Created: 10/28/15
Example for you to try 0 When we roll a die there are six possible outcomes 0 123456 I EventA The di come up even I 2 4 6 I Event B The di comes up odd I 1 3 5 I Event C The di comes up 6 I 6 0 List the outcomes in I a Not A AC I 1 3 5 I b A amp C I 6 I c A or C I 2 4 6 I d B amp C I This is just empty because nothing in common I Or 2 Union amp intersection Example General Addition Rule 0 A check of dorm rooms on a large college campus revealed that 38 had refrigerators 52 had TV39s and 21 had both a TV and a refrigerator Draw a Venn diagram to help you find each of the probabilities below 0 What39s the probability that a randomly selected from room has a TV or a refrigerator I A just refrigerator I B just TV I PA 38 I PB 52 I PAampB 21 I PA or B I PA PB PAampB Solution EventA Dorm room has TV Event B Dorm room has refrigerator PAO52 PBO38 PA amp BO21 We need to find PA or B o PA or BPAPBPA amp B052038 021069 o The probability that a randomly selected dorm room has a TV or a refrigerator is 069 Mutually Exclusive events 0 Two events A and B are mutually exclusive also known as disjoint if they do not have any common outcomes In other words they cannot occur at the same time o If events A and B are mutually exclusive then 0 PA amp B 0 0 And 0 PA or B PA PB gt The special addition rule Example Special Additive Rule 0 There are five sales associates on duty in a Staples office supply store three women Maggie Linda Vanessa and two men Derek Mike An experiment consists of classifying the next customer s action Heshe will make a purchase from one of the sales associates or buy nothing What is the probability the next customer buys from Maggie or Mike Probabilit Buy from Maggie 008 Buy from Linda 012 Buy from Vanessa 010 Buy from Derek 025 Buy from Mike 015 Buy nothing 030 Solution o LetA denote the event the customer buys from Maggie PA or BPAPB008015023 The probability the next customer buys from Maggie or Mike is 023 o Let B denote the event the customer buys from Mike 0 We need to look for PA or B 0 Since PA or BPAPBPAampB we next look for PA PB and PAampB o PA008 o PB015 o PA amp B0 since they cannot happen at the same time 0 Then 0 O Conditional Probability o Finding the probability of an event when you know the outcome is in some particular part of the sample space o PA B PAamp B PB When eventsA and B are independent we have 0 PA B PA 0 And PA amp B PA X PB gt Multiplication Rule I The quotIquot is a vertical line between A and B 0 Simple Illustration m Year in College Barrett College Brady Manning Kelly McLovin Proof 1st 2nd 1st 3rd YES YES NO NO We label PA B as equation 1 When A and B are independent PA BPA and equation 1 becomes PA Multiple both sides by PB we obtain PAgtltPBPA amp B Example An experiment consists of rolling a fair sixsided die once and recording the number faceup Given an odd number was rolled what is the probability of rolling a one 1 2 3 4 5 6 I A Odd I B l I If means it is a conditional problem P1 IA 2 P1 ampAO PA PA 36 05 P1 amp A 16 0 Solution EventA Obtaining an odd number Event B Obtaining one PAO5 Sample space 1 2 3 4 5 6 A 1 3 5 B 1 Then A amp B 1 PA amp B 16 PB A PA amp 3 PB 16 16 1


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