Statistics Formula Sheet
Combinations (order doesn’t matter)
𝑛 C𝑟
𝑛!
𝑛
=( )=
𝑟
𝑟! (𝑛 − 𝑟)!
Permutations (order matters)
𝑛P𝑟
=
𝑛!
(𝑛 − 𝑟)!
Combined Events
𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)
Mutually Exclusive Events
𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)
Conditional Probability
𝑃(𝐴|𝐵) =
𝑃(𝐴 ∩ 𝐵)
𝑃(𝐵)
Independent Events
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴) ⋅ 𝑃(𝐵)
Expected Value
𝑛
∑ 𝑥𝑖 ⋅ 𝑃(𝑥𝑖 )
𝑖=1
Z-score
𝑧 =
𝑥−𝜇
𝜎
Variance and Expected Value
Var(𝑥) = 𝐸(𝑥 2 ) − [𝐸(𝑥)]2