Probability Theory
Visual guide to probability concepts · 확률론 시각 가이드
1. Basic Probability
Probability of an event = favorable outcomes / total outcomes. P(A) ranges from 0 (impossible) to 1 (certain).
A common mistake is confusing "unlikely" with "impossible." A 1% chance event will happen about once every 100 trials. In a deck of 52 cards, the probability of drawing an ace is 4/52 = 1/13 ≈ 7.7%.
"가능성이 낮다"와 "불가능하다"를 혼동하지 마세요. 1% 확률의 사건은 약 100번 시행 중 1번 발생합니다. 52장 카드에서 에이스를 뽑을 확률은 4/52 = 1/13 ≈ 7.7%입니다.
2. Conditional Probability
P(A|B) = P(A∩B) / P(B). The probability of A given that B has already occurred.
Conditional probability explains why "streaks" feel surprising. If you flip a fair coin and get 5 heads in a row, P(next flip = heads) is still 50% — each flip is independent. But P(6 heads in a row from the start) = 1/64 ≈ 1.6%.
조건부 확률은 "연속"이 왜 놀랍게 느껴지는지 설명합니다. 공정한 동전을 던져 앞면이 5번 연속 나와도 다음 확률은 여전히 50%입니다. 하지만 처음부터 6번 연속 앞면일 확률은 1/64 ≈ 1.6%입니다.
3. Bayes' Theorem
Bayes' theorem reverses conditional probability: P(A|B) = P(B|A)·P(A) / P(B). It updates beliefs with new evidence.
Bayes' theorem is counterintuitive. Even with a 99% accurate medical test, if the disease is rare (1% prevalence), a positive result only means ~50% chance of actually having it. This is the "base rate fallacy."
베이즈 정리는 반직관적입니다. 99% 정확한 의료 검사라도 질병이 희귀하면(유병률 1%), 양성 결과가 나와도 실제 감염 확률은 ~50%에 불과합니다. 이것이 "기저율 오류"입니다.
4. Binomial Distribution
B(n,p): probability of k successes in n independent trials. P(X=k) = C(n,k)·pᵏ·(1−p)ⁿ⁻ᵏ.
The binomial distribution models yes/no scenarios: free throw success rates, defective items in manufacturing, or click-through rates in marketing. As n grows large, it approximates a normal distribution (central limit theorem).
이항분포는 자유투 성공률, 제조 불량률, 마케팅 클릭률 등 예/아니오 시나리오를 모델링합니다. n이 커지면 정규분포에 근사합니다(중심극한정리).