A bag contains four tickets marked with numbers 112, 121, 211, 222. One ticket is drawn at random from the bag. Let E_i (i = 1, 2, 3) denote the event that i^th digit on the selected ticket is 2, then which of the following is not correct ?

E_1, E₂ and E₃ are independent

$P\left(E_1\right)=\frac{2}{4}=\frac{1}{2}, P\left(E_2\right)=\frac{2}{4}=\frac{1}{2}, P\left(E_3\right)=\frac{2}{4}=\frac{1}{2}$

$P\left(E_1 \cap E_2\right)=\frac{1}{4}=P\left(E_1\right) .\left(E_2\right)$

$\Rightarrow$ '$E_1$'  and  '$E_2$' are independent.

$P\left(E_1 \cap E_3\right)=\frac{1}{4}=P\left(E_1\right) .\left(E_3\right)$

$\Rightarrow$ '$E_1$'  and  '$E_3$'  are independent.

$P\left(E_2 \cap E_3\right)=\frac{1}{4}=P\left(E_2\right) .\left(E_3\right)$

$\Rightarrow$ '$E_2$' and '$E_3$' are independent.

$P\left(E_1 \cap E_2 \cap E_3\right)=\frac{1}{4} \neq P\left(E_1\right) . P\left(E_2\right) .\left(E_3\right)$

$\Rightarrow E_1, E_2$  and  $E_3$  are not independent.