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.
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).