if A,B,C are mutually exclusive and exhaustive events and it is known that P(A U B ) = 0.63 . calculate P (C) 

Dear Student,

Given that A,B,C are mutually exclusive and mutually exhaustive events so this means , 

P(ABC)=P(S)=1    Because A,B,C are mutually exhaustive eventsP(ABC)=P(AB)=P(BC)=P(AC)=0  Because A,B,C are mutually exclusive eventsWe know,P(ABC)=P(A)+P(B)+P(C)-P(AB)-P(BC)-P(AC)+P(ABC)1=P(A)+P(B)+P(C)-0-0-0+01-P(A)-P(B)=P(C)1-P(A)+P(B)=P(C)1-P(AB)+P(AB)=P(C)1-(0.63)=P(C)(Because P(A)+P(B)-P(AB)=P(AB))So, P(C)=0.37

Regards

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