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Rework problem 5 from section 3.1 of your text, involving events E, F, and G in...

Rework problem 5 from section 3.1 of your text, involving events E, F, and G in a sample space S. Assume that Pr[E]=0.4, Pr[F]=0.45, Pr[G]=0.5, Pr[E∩F]=0.15, Pr[E∩G]=0.2, and Pr[F∩G]=0.25. Find the following probabilities: (1) Pr[E∪F]= equation editorEquation Editor (2) Pr[F′∩G]= equation editorEquation Editor (3) Pr[E′∩G′]= equation editorEquation Editor

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Answer #1

Pr[E]=0.4

Pr[F]=0.45

Pr[G]=0.5

Pr[EF]=0.15

Pr[EG]=0.2

Pr[FG]=0.25

1)Pr[EF]=Pr[E]+Pr[F]-Pr[EF]=0.45+0.4-0.15=0.7

2)Pr[F'G]=Pr[G]-Pr[FG]=0.5-0.25=0.25

3)Pr[E'G']=1-Pr[E]-Pr[G]+Pr[EG]=1-0.4-0.5+0.2=0.3

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