I'm trying to find the solution for this problem:
There are 2 urns: urn 1 has 2 red balls and 1 blue ball and urn 2 has 1 red ball and 2 blue balls. You're supposed to randomly select one urn and put your hand inside it to retrieve a ball.
What is the probability you chose urn2, if a blue ball was retrieved?
Though I have been unable to solve it, I have tried reasoning it out like this:
There are 6 total possibilities since there are 6 balls. There are 2 blue balls in urn 2. There are 2 urns. Therefore: (2 blue balls / 6 total balls) * 2 urns = 2/3
I would appreciate any help. Thanks.