behavioral · importance: critical
Essential Probability Formulas
Most undergraduate probability reduces to six formulas: addition rule, multiplication rule, conditional probability, Bayes' theorem, permutations, and combinations. The hard part is reading the word problem carefully enough to know which one to apply.
When the method applies
- • Confused about when to multiply vs add
- • Cannot tell independent from mutually exclusive
- • Bayes' theorem looks intimidating
- • Combinatorics: nCr vs nPr confusion
Common mistakes
- • Misreading "and" vs "or" in the problem
- • Forgetting to check independence assumption
- • Wrong sample space
Step-by-step method
- • P(A or B) = P(A) + P(B) − P(A and B)
- • P(A and B) = P(A) · P(B) if A, B independent
- • P(A | B) = P(A and B) / P(B) — conditional probability
- • Bayes: P(A | B) = P(B | A) · P(A) / P(B)
- • Permutations: nPr = n! / (n−r)! (order matters)
- • Combinations: nCr = n! / (r!·(n−r)!) (order does not)
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Build long-term fluency
- • Always draw a tree diagram for multi-stage events
- • Write down the sample space explicitly
- • Practice 20 Bayes problems — medical-test cases are classic
Edge cases & deeper reading
For continuous random variables, you need calculus (PDF integration). For Markov chains, you need linear algebra. Discrete probability covers most intro courses.
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