The GATE Grind

GATE 2015 EC – Question 13

Engineering Mathematics · Probability and Statistics · 1 mark · Multiple choice

Suppose $A$ and $B$ are two independent events with probabilities $P(A) \neq 0$ and $P(B) \neq 0$. Let $\bar{A}$ and $\bar{B}$ be their complements. Which one of the following statements is FALSE?

  1. $P(A \cap B) = P(A)P(B)$
  2. $P(A|B) = P(A)$
  3. $P(A \cup B) = P(A) + P(B)$
  4. $P(\bar{A} \cap \bar{B}) = P(\bar{A})P(\bar{B})$

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Show answer and explanation

Correct answer: (C) $P(A \cup B) = P(A) + P(B)$

Explanation

Independence gives A, B and D. For any two events $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, and for independent events with non-zero probabilities $P(A \cap B) \neq 0$, so the plain sum is false.