GATE CE 2025 Set 2 — Question 22
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Engineering Mathematics → Probability → Conditional Probability
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Question
Given that and are not null sets, which of the following statements regarding probability is/are CORRECT?
Correct answer
(B) Conditional probability, P(A B) = 1 if B ⊂ A.; (C) P(A ∪ B) = P(A) + P(B), if A and B are mutually exclusive.
Solution
Step-by-step evaluation:
- (A) For mutually exclusive events, . The expression is for independent events. Incorrect.
- (B) . If , then , so . Correct.
- (C) By the addition rule, . For mutually exclusive events, , so . Correct.
- (D) For independent events, . Since and are not null sets, . Incorrect.
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