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.!!!

!

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.!