Suppose A and B are two independent events with probabilities P(A) ≠ 0 and P(B) ≠ 0. Let overline A and overline B be their complements. Which one of the following statements is FALSE?

This question belongs to Engineering Maths Probability And Statistics

Probability and Statistics

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

A) $${\text{P}}\left( {{\text{A}} \cap {\text{B}}} \right) = {\text{P}}\left( {\text{A}} \right){\text{P}}\left( {\text{B}} \right)$$ B) $${\text{P}}\left( {\frac{{\text{A}}}{{\text{B}}}} \right) = {\text{P}}\left( {\text{A}} \right)$$ C) $${\text{P}}\left( {{\text{A}} \cup {\text{B}}} \right) = {\text{P}}\left( {\text{A}} \right) + {\text{P}}\left( {\text{B}} \right)$$ D) $${\text{P}}\left( {\overline {\text{A}} \cap \overline {\text{B}} } \right) = {\text{P}}\left( {\overline {\text{A}} } \right){\text{P}}\left( {\overline {\text{B}} } \right)$$

Answer & Solution

Correct Answer: Option C

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Suppose A and B are two independent events with probabilities P(A)...

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

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