The contents of 3 urns are: 1 white, 2 red, 3 green balls; 2 white, 1 red, 1 green balls and 4 white, 5 red, 3 green balls. Two balls are drawn at random. These are found to be one white and one green. Find the probability that the balls so drawn came from the third urn.
I have the answer and solution using Bayes theorem. But I would like to know how to solve it without the help of Bayes theorem, could you please explain the solution and logic.