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# Class Note for MATH 1313 with Professor Flagg at UH

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This 4 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 14 views.

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Date Created: 02/06/15

Math 1313 Section 76 Bayes Theorem In section 75 we were interested in nding the probability of the second event on the tree diagram if we knew that the rst event had occurred In this section we reverse the roles If we know that the second event occurred what is the probability of a given outcome of the rst event We can use a principle called Bayes Theorem to solve problems of this type This theorem is an application of conditional probability We ll use the conditional probability formula and the product rule to solve these problems 9 mm POMS Mm Example 1 Three factories A B and C produce engine components Factory A produces 40 of the total components Factory B produces 35 and Factory C produces the remaining 25 A quality control analysis shows that 6 of the components from Factory A do not meet speci cations 5 from Factory B do not meet speci cations and 4 from Factory C do not meet speci cations A component is selected at random from total output and is found to be defective What is the probability that it was produced at Factory A PPM POAVMA Farm 1 gl 71 60319 quot4 X39OZ M A W amt WWO 73 ma Jr 53399 gf l Math 1313 Class Notes 7 Section 76 Page 1 of4 X o LaQ flaw P M7145 fl K40LD3SX03 ltW Example 2 In a recent senatorial election 50 of the voters in a certain district were registered Democrats 35 were registered Republicans and 15 were registered Independents The incumbent Democratic senator was reelected over her Republican and Independent challengers Exit polls showed that she gained 75 of the Democratic vote 25 of the Republican vote and 30 of the Independent vote Assuming that the exit poll was accurate what is the probability that a vote for the incumbent was cast by a regist red Republican WV W p 99 PfEa nfr r 9970 I m W 2915 25gtlt35152lt3 1 35 A225 KRWW H Sx sfr QSXBQHS K3 Math 1313 Class Notes 7 Section 76 Page 2 of4 7 9 LF Example 3 A screening test has been used to determine if a person has a certain vision impairment Among people Who have the vision problem the screening test has been shown to be accurate 92 of the time The test gives a false positive reading 8 of the time ie detects the condition among people Who do not actually have it The vision impairment affects 7 of the population a Suppose a person test positive for the condition What is the probability that the person actually has the condition b Find the probability that a person tests negative for the condition but actually has it 7679 q Ck pYU G7 0 W03 a 7 ad P iam 39 P09 W Wgt M b 47 007x 72 373 gt80 t tO HON Neg n Howe 30 00 X 0 bOOQQ 907 ask ac3 Math 1313 Class Notes 7 Section 76 Page 3 of4 Example 4 Anurn contains 10 green balls and 6 blue balls Two balls are drawn in succession and without replacement What is the probability that a the second ball drawn was blue b the rst ball drawn was green given that the second ball drawn was blue c the second ball drawn was green d the rst ball drawn was gree given that the second ball drawn was Q 32 2 89 B y 4 56 i g 6W 0 0 61082 6 6 03 M883 7 72quot WAG 01 Si182 b375 Q 9amp0de green I New 82gt p 8623 c S J W652 437 if gags amp t ilt3 ClKassNogie2ion76FP age4of4 L142 iquot 0 g D Q r a i H quotIt ig m 3

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