Question 197
Urn $A$ contains $4$ white balls and $2$ red balls. Urn $B$ contains $3$ red balls and $3$ black balls. An urn is randomly selected, and then a ball inside of that urn is removed. We then repeat the process of selecting an urn and drawing out a ball, without returning the first ball. What is the probability that the first ball drawn was red, given that the second ball drawn was black?