A.

B.

C.

D.

Solution:

A.

Explanation:

Let represent the event in which A speaks the truth, represent the event in which A lies, and represent the event in which it appears head.

As a result, .

and are events that are complementary to one another.

Then

If you toss a coin, it may land on its head or tail.

As a result, whether A tells the truth or lies, the likelihood of getting head is .

Given that A tells the truth, the probability that there was head is .

We have used Bayes’ theorem to arrive at our conclusion.

Substituting the values, we now have

Consequently, the right response is (A).