On an intriguing urn probability problem

We discuss an urn probability problem, which has recently appeared on social media as a puzzle, whose analysis necessitates a prior opinion on the urn contents, and has much pedagogical merit. The derived calculations are intuitively challenging and vary to a significant extent as a function of the given prior distribution. Finally, we contrast solutions for sampling with and without replacement settings, revealing a paradoxical situation with independent draws achieved without replacement and dependent draws achieved with replacement.