Consider an experiment of a single throw of a pair of unbiased normal dice. Let three events ${\epsilon }_1,\mathrm{}\mathrm{}{\epsilon }_2$ and ${\epsilon }_3$ are defined as follows
${\epsilon }_1:$ getting prime numbered face on each dice
${\epsilon }_2:$ getting the same number on each dice
${\epsilon }_3:$ getting the sum of 4 on two dice
Which of the following is not true?

• A

  The probabilities $P\left({\epsilon }_1\right),P\left({\epsilon }_2\right),P\left({\epsilon }_3\right)$ are in arithmetic progression.
• B

  The events ${\epsilon }_1$ and ${\epsilon }_2$ are dependent
• Correct answer
  C

  $P\left(\frac{{\epsilon }_3}{{\epsilon }_1}\right)=\frac{2}{9}$
• D

  $P\left(\frac{{\epsilon }_3}{{\epsilon }_1}\right)=\frac{1}{9}$

Hence, the correct answer is option: 'C'.