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📐 Mathematics  ·  Probability (Class 11)  ·  JEE

Why is P(at least one) usually computed via the complement?

Answer: The complement 'none' is a single scenario, while 'at least one' splits into many separate cases.

  • A The complement always produces a larger and therefore safer probability value
  • B The complement 'none' is a single scenario, while 'at least one' splits into many separate cases
  • C The complement rule is the only exact method available for such events
  • D 'At least one' events are always impossible to count directly in principle

Correct answer: B. The complement 'none' is a single scenario, while 'at least one' splits into many separate cases

Explanation: Counting 'exactly one', 'exactly two' and so on is laborious, whereas 'none' is a single case, so 1 − P(none) is far quicker and less error-prone.

Concept context

Random experiments, sample space, events, and the axiomatic approach to probability

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