A release-checked easy problem for training Law of Total Probability, Combinations and Permutations, Conditional Probability.
Question
You have a box with $5$ green and $6$ orange balls. You also have a bucket with $3$ green and $7$ orange balls. If you randomly select a ball from the box and randomly select a ball from the bucket, what is the probability that the two balls are different colors?
Practice focus
This Probability problem is tagged Law of Total Probability, Combinations and Permutations, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.