Probability · JEE Main previous year questions

2016 1 question

1. Q142016 · 3 Apr 2016 · Shift 1

   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 $\mathbf{NOT}$ true?

   1. A.$E_1\text{ and }{E}_2\text{ are independent.}$
   2. B.$E_2\text{ and }{E}_3\text{ are independent.}$
   3. C.$E_1\text{ and }{E}_3\text{ are independent.}$
   4. D.$E_1,E_2\text{ and }{E}_3\text{ are independent.}$
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   Answer: D