Chapter 15 Summary & Examples Name __________________________________ General “Rules” for Probability: 1. For any event A: _____ _____ 2. If S is the entire sample space: _____ 3. For any event A: __________ 4. In general, if A and B are any two events (disjoint or not) then: ______________________ 5. If A and B are independent events then: _______ and _______ 6. In general, if A and B are any two events (independent or not) then: __________________ EXAMPLES 1. In a large Statistics class, 20% of the class earned an “A” on the first exam, 25% earned an “A” on the second exam and 16% earned an “A” on both. If a student is drawn at random from this class, find each of the following probabilities. A. The student earned an “A” on at least one exam. B. The student earned an “A” on exactly one of the exams. C. The student earned an “A” on exactly one of the exams. D. The student did not earn an “A” on either of the exams. Let F = the event that the student earned an “A” on the first exam S = the event that the student earned an “A” on the second exam E. Are F and S disjoint? Explain. F. Are F and S independent? Explain.

Chapter15(Summary&Examples( ( ( Name( ( General“Rules ...wp.lps.org/gvifquai/files/2012/08/Chapter-15-Day-2-Summary-with-Examples.pdfChapter15(Summary&Examples( ( ( Name(_____((General“Rules”forProbability:(!

Download PDF Report

Upload
others
View
2
Download
0

Embed Size (px)

Citation preview

Page 1: Chapter15(Summary&Examples( ( ( Name( ( General“Rules ...wp.lps.org/gvifquai/files/2012/08/Chapter-15-Day-2-Summary-with-Examples.pdfChapter15(Summary&Examples( ( ( Name(_____((General“Rules”forProbability:(!

Chapter(15(Summary(&(Examples( ( ( Name(__________________________________((General(“Rules”(for(Probability:(!

1.!For!any!event!A:!!!_____! !_____! ! !

!2.!If!S!is!the!entire!sample!space:! !_____!

!3.!For!any!event!A:!!! !__________!

!4.!In!general,!if!A!and!B!are!any!two!events!(disjoint-or-not)!then:! ______________________!

!5.!If!A!and!B!are!independent!events!then:!! !_______!!and!! !_______!

!!6.!In!general,!if!A!and!B!are!any!two!events!(independent-or-not)!then:! __________________!

!! ! !!!EXAMPLES( (( (

1.!!In!a!large!Statistics!class,!20%!of!the!class!earned!an!“A”!on!the!first!exam,!25%!earned!an!“A”!on!!!!!!!!!the!second!exam!and!16%!earned!an!“A”!on!both.!If!a!student!is!drawn!at!random!from!this!class,!!!!!!!find!each!of!the!following!probabilities.!!

! A.!!The!student!earned!an!“A”!on!at!least!one!exam.!!!! B.!!The!student!earned!an!“A”!on!exactly!one!of!the!exams.!!!! C.!!The!student!earned!an!“A”!on!exactly!one!of!the!exams.!!! !! D.!!The!student!did!not!earn!an!“A”!on!either!of!the!exams.!!!!!!!!Let!F!=!the!event!that!the!student!earned!an!“A”!on!the!first!exam!!!!!!!!!!!!!!S!=!the!event!that!the!student!earned!an!“A”!on!the!second!exam!!

! E.!!Are!F!and-S!disjoint?!Explain.!!!!! F.!!Are-F!and-S!independent?!Explain.!!!

Page 2: Chapter15(Summary&Examples( ( ( Name( ( General“Rules ...wp.lps.org/gvifquai/files/2012/08/Chapter-15-Day-2-Summary-with-Examples.pdfChapter15(Summary&Examples( ( ( Name(_____((General“Rules”forProbability:(!

2.!Common!sources!of!caffeine!are!coffee,!tea,!and!cola!drinks.!Suppose-that….!

!!!!!55%!of!adults!drink!coffee!!!!!!!!!!!!!25%!of!adults!drink!tea! !45%!of!adults!drink!cola!

!!!!!Suppose-also-that…-

!!!!!15%!drink!both!coffee!and!tea!!!!!25%!drink!both!coffee!and!cola!

!!!!!5%!!drink!all!three!!! !!!!!!!!!!!!5%!drink!tea!only!

!!!!!!!! A.!What!percent!of!adults!drink!cola!only?!!!! B.!!What!percent!drink!none!of!the!beverages?!!!!!!!!!!!3.!!In!April!2003,!Science!magazine!reported!on!a!new!computer!based!test!for!ovarian!cancer,!“clinical!!!!!!!proteomics,”!that!examines!a!blood!sample!for!the!presence!of!certain!patterns!of!proteins.!!Ovarian!!!!!!!cancer,!though!dangerous,!is!very!rare,!afflicting!only!1!of!every!5000!women.!!The!test!is!highly!!!!!!!sensitive,!able!to!correctly!detect!the!presence!of!ovarian!cancer!in!99.97%!of!women!who!have!the!!!!!!!disease.!!However,!it!is!unlikely!to!be!used!as!a!screening!test!on!the!general!population!because!the!!!!!!!test!gave!false!positives!5%!of!the!time.!!Why!are!false!positives!such!a!big!problem?!!Draw!a!tree!!!!!!!!!!diagram!and!determine!the!probability!that!a!woman!who!tests!positive!using!this!method!actually!!!!!!!has!ovarian!cancer.!