Probability
Addition Theorem
IIT-JEE 2013
Grade 12
Question:
Let $A$ and $B$ be two events such that $P(A \cup B)' = \frac{1}{6}$, $P(A \cap B) = \frac{1}{4}$ and $P(A') = \frac{1}{4}$. Then the events $A$ and $B$ are:
(1) mutually exclusive
(2) independent
(3) equally likely
(4) dependent but not equally likely
Step-by-Step Solution
Key Concept: First obtain $P(A)$, $P(B)$, and $P(A \cup B)$ from the given data using $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, then check whether $P(A \cap B) = P(A) P(B)$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)