Probability
Mutually Exclusive Events, Independent Events
jee_main_2026_april_4_shift_2
Grade 12
Question:
If A and B are mutually exclusive events with P(A) = 0.2 and P(B) = 0.3, and P(C) = 0.5 where C is independent of A and B, find P(A ∪ B ∪ C).
A. 0.25
B. 0.5
C. 0.75
D. 1
Step-by-Step Solution
Key Concept: For mutually exclusive A and B, P(A∪B) = P(A) + P(B). Then use independence with C.
Step 1: P(A∪B) = 0.2 + 0.3 = 0.5. Step 2: Since C is independent of A and B, P((A∪B)∩C) = P(A∪B)P(C) = 0.5 × 0.5 = 0.25. Step 3: P(A∪B∪C) = 0.5 + 0.5 - 0.25 = 0.75.
Correct Answer: C
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