involving events E, F, and G in a sample space S. Assume that Pr[E]=0.5, Pr[F]=0.6, Pr[G]=0.55, Pr[E∩F]=0.35, Pr[E∩G]=0.35, and Pr[F∩G]=0.4. Find the followin

Question

(1) Pr[E∪F]=


(2) Pr[F′∩G]=


(3) Pr[E′∩G′]=

Answer 1

(1) Pr[E∪F]: Add the two probabilities, which includes the intersection twice, then subtract the intersection so it will only be counted once.  Pr[E] + Pr[F] - Pr[E∩F]=0.5 + 0.6 - 0.35 = 0.75.

(2) Pr[F′∩G]: The Part of G that does not include F. Need to know how much of G includes F, then subtract that amount from G.    Pr[G]=0.55. Pr[F∩G]=0.4.  0.55 - 0.4 = 0.15. 

 

(3) Pr[E′∩G′]: The part that is outside both E and G.  Need to subtract Pr[E∪G] from the universe.  1 - Pr[E∪G] = 1 - ( Pr[E] + Pr[G] - Pr[E∩G]) = 1 - (0.5 + 0.55 - 0.35) = 1 - 0.7 = 0.3 = Pr[E′∩G′].