Poisson & Inverse Poisson Probability Calculator

This example demonstrates how the Poisson distribution assigns probabilities to discrete counts for a chosen rate parameter λ, visualized using a histogram/bar chart. It also showcases the inverse Poisson task: given a target cumulative probability level, it computes the corresponding quantile/threshold value. The main mathematical concepts are the Poisson probability mass function, the distribution/cumulative probability idea for discrete random variables, and solving the inverse probability problem (finding the smallest k or the matching integer outcome that satisfies a probability condition). Construction-wise, it uses GeoGebra commands Poisson to generate the probability values, BarChart to display them as a bar chart, and InversePoisson to compute the inverse result; multiple text objects are used to label λ, probability inputs, and computed outputs. Suitable for high school advanced classes and introductory college probability & statistics, especially for visualization-based learning and interactive exploration with parameter changes.