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Pulsified333
 one year ago
events E, F, and G in a sample space S. Assume that Pr[E]=0.4, Pr[F]=0.45, Pr[G]=0.45, Pr[E∪F]=0.6, Pr[E∪G]=0.65, and Pr[F∪G]=0.7. Find the following probabilities:
(1) Pr[E′∪F]=
(2) Pr[F′∩G]=
(3) Pr[E∩G]=
Pulsified333
 one year ago
events E, F, and G in a sample space S. Assume that Pr[E]=0.4, Pr[F]=0.45, Pr[G]=0.45, Pr[E∪F]=0.6, Pr[E∪G]=0.65, and Pr[F∪G]=0.7. Find the following probabilities: (1) Pr[E′∪F]= (2) Pr[F′∩G]= (3) Pr[E∩G]=

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0P(E∪G)=p(E)+P(G)P(E∩G) 0.65=0.4+0.45P(E∩G) P(E∩G)=0.850.65=0.2

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0is that for (F'∩G)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now we make make a list of probabilities: Pr[E]=0.4, Pr[F]=0.45, Pr[G]=0.45, Pr[E∪F]=0.6, Pr[E∪G]=0.65, Pr[F∪G]=0.7. P(E∩G)=0.2 P(F∩G)=0.2 p(E∩G)=0.2

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0(1) Pr[E′∪F]= .6? (2) Pr[F′∩G]= .2? (3) Pr[E∩G]= .2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now we start to find P(E′∪F)=P(E′)+P(F)P(E'∩G) THE third one is true but we are asking for P(E'∩G) not p(E∩G)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry.P(E′∪F)=P(E′)+P(F)P(E'∩F) .P(E′∪F)=0.6+0.45P(E')*P(F) .P(E′∪F)=0.6+0.450.27=0.78 i used these rules:P(A)=1P(A') when A and B are independent :P(A∩B)=P(A)*P(B)

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0how would you find #2 then?

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0did you make a venn diagram?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when two events are independent P(A∩B)=P(A)*P(B)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(1) Pr[E′∪F]= 0.78 (2) Pr[F′∩G]= 0.2475 (3) Pr[E∩G]= 0.2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0every human can make mistakes.can you explain why the first one isn't correct?

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0is it because of P(E')*P(F)

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0where did .27 come from?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0p(E'∩F)=P(E')*P(F)=(1P(E))*P(F)=(10.4)*0.45=0.6*0.45=0.27

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0but then I don't see why its the wrong answer

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.0for the first one, \(P[E\cup F] = P[F]+P[E]P[E\cap F]\) \( P[E\cup F] P[F]= P[E]P[E\cap F]\) \(P[E' \cap F] = 1(P[E]P[E\cap F]) =1 P[E\cup F] +P[F]\) Please draw a venn diagram if you cannot clarify
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