Question

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 ?

Answer 1

Let, event   E₁  : choosing first two,headed) coin

E₂ : choosing 2nd (biased) coin

E₃ : choosing 3rd biased) coin