Quick Recap — Statistics & Probability (Hard)

Chain the tools: the shortcut variance ∑x2n−xˉ2\tfrac{\sum x^2}{n}-\bar x^2, scaling/shifting effects, complement tricks (P(at least one)=1−P(none)P(\text{at least one})=1-P(\text{none})), and the binomial mean/variance. Many are numerical-value (Section B), with cross-topic links to permutations and combinations.