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# Class Note for MATH 1313 with Professor Flagg at UH

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 13 views.

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Date Created: 02/06/15
Math 1313 Section 73 Rules of Probability In this section you will learn five rules that you can use to compute probabilities Here they are Let S be the sample space of an experiment and suppose E and F are events of the experiment Rule 1 PE Z Ofor all E Rule 2 PS 1 Rule 3 HE and F are mutually exclusive events then PE U F PE PF Rule 4 If E and F are any two events of an experiment then PEUF PEPF PEnF Rule 5 If E is an event of an experiment and E 5 denotes the complement of E then PE PE 1 and therefore PE 1 PE and PE1 PE We will use Rules 3 4 and 5 extensively in solving the problems in this lesson Example 1 The SATMath scores of the senior class at a high school are shown in the table Range of Scores of Students in that Range of Scores x gt 700 23 600 lt x S 700 87 500 lt x S 600 156 400 lt x S 500 318 300 lt x S 400 94 x lt 300 22 a Construct the probability distribution for this data Math 1313 Class Notes 7 Section 73 Page 1 of5 b If a student is selected at random what is the probability that his score was i more than 500 ii less than or equal to 400 iii greater than 400 but less than or equal to 700 Example 2 Suppose a card is drawn from a wellshuf ed deck of 52 playing cards LetE be the event that the card is a face card LetF be the event that the card is a heart Find PE UF Find the probability that the card is either a 4 or a 7 Find the probability that the card is a heart or a diamond Math 1313 Class Notes 7 Section 73 Page 2 of5 Example 3 Among 500 freshmen enrolled in the business school 320 are taking an economics class 225 are taking a math class and 140 are enrolled in both What is the probability that a student selected at random from this group is enrolled in a economics andor math b exactly one ofthese courses c neither ofthese courses Example 4 Let E and F be two events of an experiment with sample space S Suppose PE 45 PF 7 and PEmF 31 Compute a PE UF b PE nF Math 1313 Class Notes 7 Section 73 Page 3 of5 c PEuF d PEuF Example 5 Let E and F be two events of an experiment with sample space S Suppose PE 38 PF 36 and PE OF 41 Compute a PE U F b PE UF 0 PEuF d PE UF Math 1313 Class Notes 7 Section 73 Page 4 of5 Example 6 You are the chief for an electric utility company The employees in your section cut down trees climb poles and splice wire You report that of the 96 employees in your section 6 cannot do any of the three management trainees 25 can cut trees and climb poles only 20 can cut trees and splice wire but cannot climb poles 10 can do all three 15 can only cut trees 12 only climb poles and a total of 30 can only do one task Find the probability that a randomly selected employee in your section can to exactly 2 tasks Find the probability that a randomly selected employee in your section cannot cut down trees Math 1313 Class Notes 7 Section 73 Page 5 of5

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