
IB Math AI SL 4.8 – Binomial Distribution
This lesson introduces students to the binomial distribution, one of the most important discrete probability models in statistics. Students learn that a binomial distribution models the number of “successes” in a fixed number of independent trials, where each trial has only two possible outcomes and a constant probability of success.
The presentation develops both the conceptual understanding and mathematical formulation of the distribution, showing how to calculate the probability of r successes, the expected value (mean), and the variance. Step-by-step proofs and worked examples guide students through the reasoning behind the formulas ( E(X) = np ) and ( Var(X) = np(1-p) ). Practice problems, such as modeling a basketball player’s free throws or testing product reliability, illustrate the real-world applications of the distribution. The lesson also emphasizes the assumptions underlying the model—fixed number of trials, independence, and constant probability—and shows how violations affect accuracy.
By the end of the lesson, students can model random processes using binomial distributions, calculate probabilities, and interpret expected outcomes and variability. Fully aligned with IB Math AI SL Topic 4.8 – Binomial Distribution, this slide deck builds a strong foundation for later topics in inferential statistics and probability-based modelling.
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