Please ans in detail   

 

 

Since they are asking about contradicting the fact,it means if A  is True ,then B should be False,and if A is false ,then B is true.Now, prob. of A speaking truth is (75/100)=3/4 i.e.P(A)=3/4 similarly,P(B)=9/10 ,Prob. of A speaking false is 1-P(A)=P(A')=1/4 ,similarly,P(B')=1-9/10=1/10

Required probability=P(A)*P(B')+P(A')*P(B)=(3/4*1/10)+(1/4*9/10)=12/40=3/10