Mistake Master
Ten Ways to Make Exactly Three, and One Formula That Counts Them
You'll learnwhy the combination coefficient belongs in the binomial formula, the four conditions a setting has to pass before you may use it, the mean np and standard deviation √(np(1−p)), and how to turn at least, more than and at most into the right sum of bars.
A player makes 70% of her free throws and takes five shots. Five shots have thirty-two possible outcomes, and this animation draws every one of them, sorted by how many went in. Ten of those thirty-two make exactly three — which is what the 10 in the formula counts, and dropping it is a factor-of-ten error. From there the six bars of the whole distribution are built twice, once from the formula and once by weighing the thirty-two paths, and the two roads land on the same six numbers. Then the words: at least 4 collects two bars, more than 4 keeps one, and at least one defective is everything except none. It ends on a club of fifteen where the conditions never held and the model misses a bar by 0.05. Twelve short steps; press Next for each one.