Explanation
Concept:
Let A1, A2, ..., An be n mutually exclusive and exhaustive events of the sample space S and A is event which can occur with any of the events then
• P (AAi)=∑i=1nP(Ai)P(AiA)P(Ai)P(AiA)
Calculations
{\mathrm{Consider,Let~K~be~the~event~that~both~A~and~B~agree,}}$
T be the event that they both A and B speak the truth
⇒P( T) = xy
L be the event that they both A and B lie
⇒P(L)=(1−x)(1−y)
To find :The probability that the statement is true = P(LT)
Let K be the event that both of them agree
P(LT)=P(T)P(TK)+P(L)P(LK)P(T)P(TK)⇒P(LT)=xy+(1−x)(1−y)xy
