A fair die is rolled. consider events E = {1, 3,5} F = {2,3} and G = {2,3,4,5}. Find
P(EG) and P(GE)
Here, the sample space si S=1,2,3,4,5,6Given,E={1,3,5},F={2,3| and G=|2,3,4,5}⇒E∩F={3},E∩G={3,5},E∩F={1,2,3,5},(E∪F)∩G=(2,3,5) and (E∩F)∩G={3}.⇒n(S)=6,n(E)=3,n(F)=2,n(G)=4n(E∩F)=1,n(E∩G)=2,n(E∩F)=4n[(E∪F)∩G]=3 and n[(E∩F)∩G]=1
∴ by the formula, Probability = Number of favourable eventsTotal number of events
We have P(E)=36=12,P(F)=26=13,P(G)=46=23P(E∩F)=16P(E∩G)=26=13p[(E∪F)∩G]=36=12 and P[(E∩F)∩G]=16
P(EG)=P(E∩G)P(G)=1323=12 and P(GE)=P(G∩E)p(E)=1312=23