# JMF-3-07 - Introduction to Probability Chapter 3 Notes Set...

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CH Reilly UCF - IEMS - STA 3032 1 Introduction to Probability Chapter 3 Notes Set 3 Spring 2007

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CH Reilly UCF - IEMS - STA 3032 2 Some preliminaries An experiment involves making an observation or a measurement. There is an outcome for every experiment that is unknown until the experiment is completed. The set of all possible outcomes of an experiment is called a sample space . Some sample spaces are finite. Sample spaces may be discrete (outcomes are countable) or they may be continuous (outcomes are uncountable).
CH Reilly UCF - IEMS - STA 3032 3 Events An event is any subset of a sample space. A simple event is any event that corresponds to a basic (or simple) outcome. Two events that cannot occur simultaneously are said to be mutually exclusive events. Any two simple events are mutually exclusive. Venn diagrams and set notation (union, intersection, complement) are commonly used to describe relationships between events.

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CH Reilly UCF - IEMS - STA 3032 4 Factorial notation 1 ! 0 that assume we ss, completene For ) 1 )( 2 ( ) 2 )( 1 ( ! 1 = - - = = = n n n i n n i
CH Reilly UCF - IEMS - STA 3032 5 What is “n!”? n! is the number of ways that n things (which could be items or people) can be arranged or ordered in n positions in a sequence. Suppose there are 5 students to be seated in 5 chairs in the front row. There are 5! = 120 different ways that the 5 students can be seated in those chairs. Factorials help us count. The alternative is to list all of the possible seating arrangements.

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CH Reilly UCF - IEMS - STA 3032 6 Counting rules So that we may calculate probabilities for events of interest, we may have to determine how many simple events are included in a sample space. We may also have to determine how many simple events are included in the event whose probability we seek to calculate. Counting simple events can be more challenging than it sounds. We have 4 rules to help us.
CH Reilly UCF - IEMS - STA 3032 7 Multiplication rule set. each from item one with sample a draw to ways are There elements. has , , , 2 , 1 , Set elements. of sets are There 2 1 1 k k i i i n n n n n k i i k = = =

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CH Reilly UCF - IEMS - STA 3032 8 Example – multiplication rule Suppose that you want to take a 4-course schedule next semester that includes a GEP course, as engineering core course, a course in your major, and an advanced statistics course. You discover there are: 23 GEP courses offered. 4 engineering core courses offered. 9 courses in your major offered. 3 advanced statistics courses offered. Choose from (23)(4)(9)(3) = 2484 schedules.
CH Reilly UCF - IEMS - STA 3032 9 Permutation rule Given n items. How many ways can r out of the n items be chosen

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## This note was uploaded on 08/22/2010 for the course STA 3032 taught by Professor Sapkota during the Spring '08 term at University of Central Florida.

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JMF-3-07 - Introduction to Probability Chapter 3 Notes Set...

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