Assume three buckets.
Bucket 1: 6 red and 4 black balls
Bucket 2: 8 red and 2 black balls
Bucket 3: 4 red and 1 black ball
Draw a ball from number 1: if red go to number 2; if black go to number 3.
1. What is probability (red on draw 2, given red on draw 1)?
2. What is probability (black on draw 2, given red on draw 1)?
3. What is probability (red on draw 2, given black on draw 1)?