Texts: From three bags:
• Bag 1 contains 4 red and 2 black balls,
• Bag 2 contains 3 red and 4 black balls,
• Bag 3 contains 2 red and 5 black balls.
The following steps are followed respectively:
Step 1: A ball is randomly drawn from Bag 1 and placed in Bag 2.
Step 2: A ball is randomly drawn from Bag 2 and placed in Bag 3.
Step 3: A ball is randomly drawn from Bag 3 and placed in Bag 1.
Step 4: A ball is randomly drawn from Bag 1.
Answer the questions below. (Write down the formulas you will use when answering.)
(a) At the end of the 3rd step, the color distribution in all three bags is similar to that at the beginning of the experiment. What are the chances of it being the same?
(b) If the ball drawn in the 4th step is black, what are the chances that the ball drawn in the 1st step is also black?