Using Card Games for Conditional Probability, Explaining Gamma vs. Poisson Distributions, and Weighing Central Limit Theory

Students taking probability course for the first time are often struggling with conditional probability. To help explain the concept better, card games are used to explain especially differences of conditional probabilities of sequential and simultaneous card draws. Several card game experiments are discussed and typical probability results are shown and compared with predictions. These simple experiments can be demonstrated in classroom and students can use them to test the predictions. Another concept students often struggle is distinguishing gamma from Poisson distribution. An identity connecting them, generalizing the connection between exponential and Poisson distribution, will be used to discuss their differences and to point out nuances in the wording of some probability problems that yield different answers when both distributions are used. Lastly, a teaching tool for explaining central limit theorem is discussed based on guessing weights of books. This guessing game proves useful to explain sampling distribution.