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Understanding AND and OR Probability

Apr 12, 2025

AND_OR Probability Lecture Notes

Overview of Probability

  • Probability measures the likelihood of an event occurring.
  • Key concepts include:
    • Sample space (S): All possible outcomes.
    • Event (E): A subset of the sample space.
    • Probability of an event: P(E) = Number of favorable outcomes / Total outcomes.

AND Probability

  • Refers to the intersection of two events.
  • Notation: P(A AND B)
  • Formula for independent events:
    • P(A AND B) = P(A) * P(B)
  • Example: Drawing cards from a deck.
    • P(A) = Probability of drawing an Ace = 4/52.
    • P(B) = Probability of drawing a King = 4/52.
    • P(A AND B) = P(A) * P(B) = (4/52)(4/52).

OR Probability

  • Refers to the union of two events.
  • Notation: P(A OR B)
  • Formula:
    • P(A OR B) = P(A) + P(B) - P(A AND B)
  • Important because it accounts for double counting of overlapping events.
  • Example: Rolling two dice and getting a sum of 7.
    • Calculate different combinations (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).

Dependent vs. Independent Events

  • Independent Events: The occurrence of one event does not affect the other.
    • Example: Flipping a coin and rolling a die.
  • Dependent Events: The occurrence of one event affects the other.
    • Example: Drawing cards without replacement.

Practical Applications

  • Used in various fields:
    • Statistics
    • Risk assessment
    • Decision making

Summary

  • Understanding AND and OR probability is crucial for analyzing complex events.
  • Key takeaway: Always consider the relationship between events (independent vs. dependent) when calculating probabilities.