Would you mind sharing the Bayesian solution to this? I always have problems with the setup of a Bayesian equation, so end up going back to first principles like this:
I used upper case letters for the ball picked from the bag of all white balls and lower case for the ball picked from the bag with fifty-fifty mix. The equally likely possibilities are:
Picked first / Picked second
w / W
b / W
W / b
W / w
We know that we can eliminate the second possibility, leaving three possibilities, two of which include a white ball picked second.