A coin is tossed.

If the coin shows head, toss it again

but if it shows tail, then throw a die.

Find the conditional probability of the event that "the die shows a number greater than 4" given that "there is at least one tail"?

I proceeded as follows:

Sample space = {(H,H), (H,T), (T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}

E = Atleast one tail = {(H,T), (T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}

F = the die shows a number greater than 4 = {(T,5),(T,6)}

E intersection F = {(T,5),(T,6)}

P(F/E) = P(E intersection F)/P(E) = (2/8) / (7/8) = 2/7. [n(A intersection B)/n(E)]

They have given the answer as 2/9.

What went wrong I do not know.

Kindly guide me.

Aranga