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.

Therefore,

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).