IB Maths AA SL 4.8 - The Binomial Distribution

This IB Maths AA SL Topic 4.8 – The Binomial Distribution resource develops students’ understanding of binomial probability models and their key statistical properties. It begins by introducing the conditions required for a binomial distribution: a fixed number of trials, two possible outcomes for each trial, independent trials, and a constant probability of success. Students learn how to use the notation X ~ B(n, p), where n is the number of trials and p is the probability of success.

The lesson then introduces the formula for calculating the probability of exactly r successes and develops students’ ability to find the mean, variance, and standard deviation of a binomial distribution using mean = np, variance = np(1 - p), and standard deviation = sqrt(np(1 - p)). Optional proofs are included for advanced students who wish to explore where these formulas come from. Students apply the distribution to real-world contexts involving basketball free throws and smartphone durability tests, including identifying suitable assumptions and interpreting expected values. With clear definitions, formula summaries, optional derivations, contextual practice questions, and fully worked solutions, this resource helps SL students build strong binomial probability skills in line with IB Mathematics AA expectations.