CBSE Class 12-science Answered
Let E be the event that the A reports that head appears in the throwing of the die and let S1 be the event that head appears and S2 be the event that head does not appear.
P(E | S1) = Probability that A reports that head appears when head has actually appeared on the coin = Probability that A speaks the truth =
P(E | S2) = Probability that A reports that head appears when head has not appeared on the coin = Probability that A does not speak the truth =
Thus, by Bayes theorem, we get
P(S1 | E) = Probability that the report of A that head has appeared is actually a head
Yes, as A speaks truth 5 times out of 9, i.e., only 55%, which is very much on lower side.