Fix the mistake: Probability 1 (Fundamentals of Probability)

Probability① Definition and Basic Properties of Probability

Probability P(A) = n(A)/n(U) (when all outcomes are equally likely)

Addition Theorem・Complementary Event

P(A∪B) = P(A) + P(B) − P(A∩B)
If mutually exclusive, P(A∪B) = P(A) + P(B)
Complementary event: P(Ā) = 1 − P(A)

Example①
Probability of rolling a multiple of 2 or a multiple of 3 on a die:
P(multiple of 2)=3/6、P(multiple of 3)=2/6、P(6)=1/6 → 3/6+2/6−1/6 = 2/3
Example② (Complementary Event)
Probability of getting at least one head with 2 coins: 1 − P(both tails) = 1 − 1/4 = 3/4
Key Points
  • “At least” → complementary event
  • 0≤P(A)≤1、P(U)=1、P(φ)=0

Practice Problems

  1. Choose one number from 1〜10. What is the probability of choosing a multiple of 3?
  2. Choose one number from 1〜20. What is the probability of choosing a multiple of 4 or 6?
  3. Roll a die twice. What is the probability that the product is even? (Use the complementary event.)

Answers

  1. 3/10
  2. 5 multiples of 4 + 3 multiples of 6 − 1 multiple of 12 = 7 → 7/20
  3. 1−P(both odd)=1−(1/2)²=3/4

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