Probability is one of the most useful math skills in daily life. Developing awareness of probability concepts and applying them appropriately is of great importance to everyone, given its instrumental role in disciplines beyond mathematics, including biology, medicine, economics, and sports. Unfortunately, studies of secondary school students reveal that the percentage of students who understand the key concept of probability was much lower than suggested by the National Assessment of Educational Progress. Many students' understanding of probability is based on preconceptions that are not aligned with established meanings. This leads to problems in decision making later in life, where almost everyone, even professional statisticians, suffers from systematic biases in judgments of probability while maintaining strong misconceptions.

Artificial Intelligence (AI) offers a setting for probabilistic problem solving that is relevant and meaningful to students, as probability is one of the mathematical concepts that are foundational to AI. Solving problems with AI often involves reasoning under uncertainty, where probability-based concepts can provide tools to explore and reach optimal decisions. For students, AI provides a modern context for connecting probability concepts to real-life situations and provides unique opportunities for transdisciplinary learning that can advance student understanding of both AI systems and probabilistic reasoning.

Until recently, there was very little knowledge and research into how to introduce AI to the K-12 population. One approach to bring AI to the K-12 classroom that has shown promise in other STEM disciplines is digital game-based learning. Since the early 2000s, much evidence points to the efficacy of game-based learning in promoting student learning, particularly of problem-solving skills. Game-based learning has been well studied in its application in math education as well. However, there is very little research into using game-based learning for AI education for youth, given that the research field of K-12 AI education is still in its infancy. Designing game-based environments with AI problem-solving offers a great opportunity to both build on and contribute to the existing knowledge of how to integrate math and AI education in K-12 classrooms through technological innovations.

In this paper, we present our educational game, "The 7th Patient", which teaches probability concepts within an environment that supports the reciprocal development of math and AI skills. We present the games' mathematical learning objectives, particularly independent and conditional probability, and how we ground those objectives within the application of Bayesian networks: identifying variables, constructing the network with probability tables, performing inference, and decision-theoretic reasoning. We conducted a study where more than 1200 high-school students played the game, and we present our findings on the games' efficacy.

Keywords: Education, math education, AI education, probability, game-based learning.