Probability that A speaks truth is 4/5 . A coin is tossed. A reports that a head appears. The probability that actually there was head is
Let E1 and E2 be the events such that
E1: A speaks truth
E2: A speaks false
Let X be the event that a head appears.
If a coin is tossed, then it may result in either head (H) or tail (T).
The probability of getting a head is 1/2 whether A speaks truth or not.
`:.P(X|E_1) = P(X|E_2) = 1/2`
The probability that there is actually a head is given by P (E1|X).