Tree Diagram.notebook

1 5

April 24, 2015

2 3

1 3

Rememberthatthe symbol∪ • means"union" • roughlytranslatesto "or" • usuallymeans"add" differentbranchesona treediagram • lookslikethisonaVenn diagram:A∪B A

Rememberthatthe symbol∩ • means"intersection" • roughlytranslatesto"and" • usuallymeans"multiply"acrossabranchonatreediagram B • lookslikethisonaVenndiagram:A ∩B A

1 5

2 3

1 3

B

P(Billswinsboth)= (4/5)(5/6)= (20/30) P(Billswinsthen Andreawins)= (4/5)(1/6)= (4/30)

P(Andreawinsthen Billwins)= (1/5)(2/3)= (4/30)

P(Andreawinsboth)= (4/5)(5/6)= (2/30)

1

Tree Diagram.notebook

April 24, 2015

(20/30) (4/30) 1 5

2 3

(4/30)

1 3

"and"onatree diagrammeans "multiply" acrossabranch while"or"ona treediagram meansadd branches together

(2/30) P(Billwinsatleastonegame) =P( BillwinsandBillwins or BillwinsandAndreawins or AndreawinsandBillwins ) =(20/30)+(4/30)+(4/30) =(14/15) =1‐P(Billwinsnone) =1‐P(AndreawinsandAndreawins) =1‐(2/30)

(20/30)

(4/30) 1 5

2 3

(4/30)

1 3

(2/30)

GiventheBill winsatleastone game,indthe probabilitythat hewinsboth games.

theword"given"or "if"signalsustouse theconditional probabilityformula

P(Billwinsboth giventhat Billwinsatleastone ) =P( B | A) =P( A∩ B)/P( A)[fromrearrangingdatabookconditionalformula) =P( Billwinsatleastone AND Billwinsboth )/P( Billwinsatleastone ) =P( Billwinsboth )/P( Billwinsatleastone ) = (4/5)(5/6)/ (28/30) = (20/30)/ (28/30) =(20/28)=5/7 2