CA Foundation Exam > CA Foundation Questions > If events A and B are independent thena)AC an...
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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?
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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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