alleryIf P(A) = 1/3, P(B) = 1/4, A and B are independent. P(A ∪ B):
A7/12 = 1/3 + 1/4 - 1/12
B7/12
C1/2
D1/12
Answer & Solution
Correct answer: A. 7/12 = 1/3 + 1/4 - 1/12
**Independence:** P(A ∩ B) = P(A)P(B) = (1/3)(1/4) = 1/12. P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 4/12 + 3/12 - 1/12 = 6/12 = 1/2. Wait — let me recompute: 1/3 = 4/12, 1/4 = 3/12, sum 7/12 minus 1/12 = 6/12 = 1/2. So actually = 1/2, not 7/12 as I wrote.
Let me re-examine options.
**Option A = 7/12 but my calc gives 6/12. The correct answer is 1/2, which is option D.**
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