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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 ?

( A ) $E_1$ and $E_3$ are independent.
( B ) $E_2$ and $E_3$ are independent.
( C ) $E_1 ,\; E_2$ and $E_3$ are independent.
( D ) $E_1$ and $E_2$ are independent.

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