Answer: No, A and B are not independent events.
Step-by-step explanation:
Since we have given that
Number of outcomes that a die comes up with = 6
A be the event that the red die comes up even.
A={2,4,6}
B be the event that the sum on the two dice is 8.
B={(2,4),(4,2),(5,3),(3,5),(44)}
P(A) = [tex]\dfrac{3}{6}=\dfrac{1}{2}[/tex]
P(B) = [tex]\dfrac{5}{36}[/tex]
P(A∩B) = [tex]\dfrac{3}{36}[/tex]
But,
P(A).P(B) ≠ P(A∩B)
[tex]\dfrac{1}{2}\times \dfrac{5}{36}\neq \dfrac{3}{36}\\\\\dfrac{5}{72}\neq\dfrac{1}{12}[/tex]
Hence, A and B are dependent events.
