Let A and B be two events such that P(A B) = 1/6 , P(A B) = 1/4 and P(A) = 1/4 . Then, events A and B are: - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live

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Let A and B be two events such that P (\overset{ˉ}{A \cup B}) = \frac{1}{6}, P (A \cap B) = \frac{1}{4} and P (\overset{ˉ}{A}) = \frac{1}{4} . Then, events A and B are:

Solution & Step-by-step Explanation

1. P (\overset{ˉ}{A}) = 1/4 ⟹ P (A) = 1 - 1/4 = 3/4 2. P (\overline{A \cup B}) = 1/6 ⟹ P (A \cup B) = 1 - 1/6 = 5/6 3. Use P (A \cup B) = P (A) + P (B) - P (A \cap B) : 5/6 = 3/4 + P (B) - 1/4 5/6 = 2/4 + P (B) ⟹ 5/6 = 1/2 + P (B) P (B) = 5/6 - 3/6 = 2/6 = 1/3 4. Check Independence: P (A) \cdot P (B) = (3/4) \cdot (1/3) = 1/4 . Since this equals P (A \cap B), events are independent.5. Check Equally Likely: P (A) = 3/4 and P (B) = 1/3 . They are not equally likely.

Try it yourself before checking the explanation above.

Let A and B be two events such that P (\overset{ˉ}{A \cup B}) = \frac{1}{6}, P (A \cap B) = \frac{1}{4} and P (\overset{ˉ}{A}) = \frac{1}{4} . Then, events A and B are:

Equally likely but not independent

Mutually exclusive and independent

Independent but not equally likely

Equally likely and mutually exclusive

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