Let two fair six-faced dice

Let two fair six-faced dice $\mathrm{A}$ and $\mathrm{B}$ be thrown simultaneously. If $\mathrm{E}_{1}$ 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?