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JEE Math Practice Question

Let two fair six-faced dice $$A$$ and $$B$$ be thrown simultaneously. If $${E_1}$$ is the event that die $$A$$ shows up four, $${E_2}$$ is the event that die $$B$$ shows up two and $${E_3}$$ is the event that the sum of numbers on both dice is odd, then which of the following statements is $$NOT$$ true?

  1. A.$${E_1}$$ and $${E_2}$$ are independent.
  2. B.$${E_2}$$ and $${E_3}$$ are independent.
  3. C.$${E_1}$$ and $${E_3}$$ are independent.
  4. D.$${E_1},$$ $${E_2}$$ and $${E_3}$$ are independent.

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