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If events A and B are independent then
  • a)
    AC and BC are dependent
  • b)
    AC and B are dependent
  • c)
    A and BC are dependent
  • d)
    AC and BC are also independent
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If events A and B are independent thena)AC and BC are dependentb)AC an...



Explanation:

Independence of Events:
Events A and B are said to be independent if the occurrence of one event does not affect the probability of the other event occurring. Mathematically, if P(A ∩ B) = P(A) * P(B), then events A and B are considered independent.

Independence of Complements:
When events A and B are independent, their complements (AC and BC) are also independent. This means that knowing whether event A occurs does not provide any information about the occurrence of event B, and vice versa.

Explanation of Options:
  • AC and BC are dependent: This statement is false as the complements of independent events are also independent.
  • AC and B are dependent: This statement is false as the complement of one event and the other event are independent when the original events are independent.
  • A and BC are dependent: This statement is false as independence of events does not change when considering different combinations of the events.
  • AC and BC are also independent: This statement is true based on the concept of independence of complements. If events A and B are independent, then their complements AC and BC are also independent.


Therefore, the correct answer is option 'D' - AC and BC are also independent when events A and B are independent.
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If events A and B are independent thena)AC and BC are dependentb)AC and B are dependentc)A and BC are dependentd)AC and BC are also independentCorrect answer is option 'D'. Can you explain this answer?
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