Probability inequality : Is the following always true?

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SUMMARY

The discussion centers on the probability inequality P(A ∪ B) ≤ P(A) + P(B), which is a fundamental property in probability theory. Participants emphasize the importance of understanding the Addition Rule in probability to grasp this inequality. The inquiry reflects a need for deeper intuition regarding the definition of probability and its application in real-world scenarios. The conversation suggests that revisiting foundational concepts can clarify the understanding of this property.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with the Addition Rule in probability
  • Knowledge of set theory and unions
  • Ability to interpret probability notation
NEXT STEPS
  • Review the Addition Rule in probability
  • Study the definitions of union and intersection of sets
  • Explore examples of probability inequalities in real-world applications
  • Learn about conditional probability and its implications
USEFUL FOR

Students of probability theory, educators teaching probability concepts, and anyone seeking to strengthen their understanding of fundamental probability properties.

michonamona
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Homework Statement



P(AUB) <= P(A) + P(B)

Homework Equations





The Attempt at a Solution



I can't understand the intuition behind this property. It's not a homework assignment, it was just something that came up in class.

Thanks,
M
 
Physics news on Phys.org
Go back to the definition, how was P(A) defined for you.
 
Have you covered the Addition Rule yet? If so, compare what you wish to show to that.
 

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