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.