A speaks truth in 60% cases and B speaks truth in 70% cases. The probability that they will say the same thing while describing a single event is

Consider the following events:A1 : A speaks truthA2 : B speaks truthThen, P(A1) = 60/100 = 3/5, P(A2) = 70/100 = 7/10.For the required event, either both of them should speak the truth or both of them should tell a lie. Thus, the required probability is=PA1∩A2∪A1∩A2=PA1∩A2+PA1∩A2=PA1PA2+PA1A2=35×710+1−351−710=0.54