There are three coins. One is a two-headed coin ( having head on both faces ), another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin?

Question

$(a)\;\large\frac{20}{47}\qquad(b)\;\large\frac{10}{47}\qquad(c)\;\large\frac{5}{47}\qquad(d)\;\large\frac{12}{47}$