GATE EC 2015 Set 1 — Question 13
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Engineering Mathematics → Probability → Conditional Probability
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Question
Suppose and are two independent events with probabilities and . Let and be their complements. Which one of the following statements is FALSE?
Correct answer
(C) P(A ∪ B) = P(A) + P(B)
Solution
Two events and are independent if .
- Statement (A) is the definition of independence, so it is true.
- Statement (B): . This is true for independent events.
- Statement (D): If and are independent, their complements and are also independent. Thus . This is true.
- Statement (C): . For to be true, must be 0 (mutually exclusive). Independence does not imply mutual exclusivity (especially since ). Thus, (C) is FALSE.
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