We have two buckets full of marbles. There are 30 red marbles and 10 black marbles in Bucket #1 and 20 red and 20 Black marbles in Bucket #2. Your friend secretly pulls a marble from one of the two buckets and shows you that the marble is red.
What is the probability that it was pulled from Bucket #1?
Let’s say your friend puts the marble back in and now picks two marbles. She draws one marble, puts it back in the same bucket, then draws a second. They both happen to be red. What is the probability that they both came from Bucket #1?