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.

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) =
`(3)/(6)=(1)/(2)`

P(B) =
`(5)/(36)`

P(A∩B) =
`(3)/(36)`

But,

P(A).P(B) ≠ P(A∩B)

`(1)/(2)* (5)/(36)\\eq (3)/(36)\\\\(5)/(72)\\eq(1)/(12)`

Hence, A and B are dependent events.