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

Given: let E1 be the event that A speaks truth, E2 be the event that A lies and X be the event that it appears head.


As E1 and E2 are the events which are complimentary to each other.

Then P (E1) + P (E2) = 1

P (E2) = 1 - P (E1)

P (E2)

If a coin is tossed it may show head or tail.

Hence the probability of getting head is 1/2 whether A speaks a truth or A lies.

P(X|E1) = P(X|E2) = 1/2

Now the probability that actually there was head, give that A speaks a truth is P(E1|X).

By using bayes’ theorem, we have:

Therefore correct answer is (A).

Next Question

If A and B are two events such that A B and P(B) ≠ 0, then which of the following is correct?

(view answer)