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📐 Mathematics  ·  Probability  ·  JEE

The probability that at least one event occurs: P(A ∪ B) = 1 - P(A' ∩ B') by:

Answer: De Morgan law and complement rule.

  • A Bayes theorem, which relates conditional probabilities
  • B De Morgan law and complement rule
  • C The multiplication rule for independent events
  • D The total probability theorem across partitions

Correct answer: B. De Morgan law and complement rule

Explanation: De Morgan's law: (A ∪ B)' = A' ∩ B'. Apply complement rule: P(A ∪ B) = 1 − P((A ∪ B)') = 1 − P(A' ∩ B'). If A,B independent: P(A' ∩ B') = P(A')P(B') = (1−P(A))(1−P(B)).

UABA and BA onlyB onlyOutside both circles: complement of (A union B)

Venn diagram of the universal set U with events A and B, showing the intersection (A and B), the parts unique to each event, and the complement region outside both.

Concept context

Chance, events, conditional probability, and Bayes theorem

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