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)?

This solution analyzes the impact of conditional probability with drawing balls from different buckets.