Suppose a girl throws a die. If she throws a 5 or 6, she tosses a coin 3 times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with a die?

Question

$(A)\;\frac{8}{11}$
$(B)\;\frac{7}{11}$
$(C)\;\frac{5}{11}$
$(D)\;\frac{3}{11}$