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 $?$

  • [JEE MAIN 2016]
  • A

    $E_1 $ and $E_3 $ are independent.

  • B

    $E_1 , E_2$  and $E_3 $ are independent.

  • C

    $E_1$and $E_2$ are independent.

  • D

    $E_2  $ and $E_3 $ are independent.

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