Question

Two fair, distinct dice (one red and one green) are rolled. Let A be the event the red die comes up even and B be the event the sum on the two dice is eight. Are A,B independent events?

Answer 1

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) = $\dfrac{3}{6}=\dfrac{1}{2}$

P(B) = $\dfrac{5}{36}$

P(A∩B) = $\dfrac{3}{36}$

But,

P(A).P(B) ≠ P(A∩B)

$\dfrac{1}{2}\times \dfrac{5}{36}\neq \dfrac{3}{36}\\\\\dfrac{5}{72}\neq\dfrac{1}{12}$

Hence, A and B are dependent events.