E₁ : {(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)}

E₂ : {(1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2)}

E₃ : {(1, 2), (1, 4), (1, 6), (3, 2), (3, 4), (3, 6), (5, 2), (5, 4), (5, 6), (2, 1), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6, 5)}

$\mathrm{P}\left({\mathrm{E}}_1\right)=\frac{6}{36}=\frac{1}{6};\mathrm{P}\left({\mathrm{E}}_2\right)=\frac{6}{36}=\frac{1}{6}$

$\mathrm{P}\left({\mathrm{E}}_3\right)=\frac{18}{36}=\frac{1}{2}$

P(E₁ $\cap$ E₂) = $\frac{1}{36}$ = P(E₁) P(E₂)

⇒ E₁ & E₂ are independent

P(E₂ $\cap$ E₃) = $\frac{3}{36}=\frac{1}{12}$= P(E₁) P(E₃)

⇒ E₂ & E₃ are independent

P(E₁ $\cap$ E₃) = $\frac{3}{36}=\frac{1}{12}$= P(E₁) P(E₃)

⇒ E₁ & E₃ are independent

P(E₁ $\cap$ E₂ $\cap$ E₃) = 0 $\ne$  P(E₁) P(E₂) P(E₃).

⇒ E₁, E₂ & E₃ are not independent.