Answer 1

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.
P(E1)=45
Therefore,
P(E2)=1-P(E1)=1-45=15

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).