combinatorial, discrete probability

disjoint

no elements in common

• A AND B = empty

sum rule

if A AND B are disjoint

• size of A U B = size of A + size of B

inclusion exclusion principle

product rule

• for a sequence of k tasks where theres n1 ways for k1, n2 for k2, the whole sequence of k tasks is done in this many ways

order matters, no repetition

• AB, AC, BA, BC, CA, CB

• n is no of options, k is the size of subset/selection

• special case if n = k, then k!

order doesn’t matter, repetition not allowed

• AB, AC, BC

n choose k

order matters, repetition allowed

• AA, AB, AC, BA, BB, BC, CA, CB, CC

n^k

• always n ways to select through k set

order doesn’t matter, repetition allowed

• AA, AB, AC, BB, BC, CC

probability distribution

likeliness of each outcome

• all between 0 and 1

• add up to 1

• uniform distribution is when all outcomes are equally likely

probability of union of 2 events E1 and E2

conditional probability

independence

bayes theorum

for questions that feel like probability tree or give relevant information