A person is known to speak truth 3 out of 4 times. He  throws a dice and responds that it is a six. Then the  probability that it is actually a six is

LetE = the event that A reports it is six E1 = six turns up when a dice is thrown E2 = six does not turns up when a dice is thrown Probability that six actually showed up if A reported that of was six =PE1/EPE1/E=PE1∩EP(E)=PE1⋅PE/E1PE1⋅PE/E1+PE2⋅PE/E2PE/E1=Probability that the person reports six when it actually showed PE/E2= Probability that the person reports six when it did not show six = Probability that he lies =1−34=14 also PE1=16 and PE2=56PE1/E=16⋅3416⋅34+56⋅14=38