question_answer

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 one of the following statements is not true?

A)  \[{{E}_{1}},\,{{E}_{2}}\,and\,{{E}_{3}}\]are independent

B)  \[{{E}_{1}},\,and\,{{E}_{3}}\] are independent

C)  \[{{E}_{2}}\,and\,{{E}_{3}}\] are independent

D)  \[{{E}_{1}},\,and\,{{E}_{2}}\] are independent

E)  None of these