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 truth Then, PA1=60/100=3/5,PA2=70/100=7/10For the required event, either both of them should speak thetruth or both of them should tell a lie. Thus, the required probability isPA1∩A2∪A¯1∩A¯2 =PA1∩A2+PA¯1∩A¯2 =PA1PA2+PA¯1A¯2 =35×710+1−351−710=0.54