Practice problem
Casework and Law of Total Probability
Let's say we have two separate buckets of balls, a red bucket and a blue bucket. The red bucket has red balls (but nothing else), while the blue bucket has blue balls (but nothing else). We want to toss a typical coin to see from which bucket we will pick from. If the coin is heads, we will pick from the red bucket, and if it is tails, we will pick from the blue bucket. What is the probability of getting a blue ball from this process?