Consider a game that consists of two successive trials The f

Consider a game that consists of two successive trials. The first trial has outcome A or B, and the second trial has outcome C or D. The probabilities of the four possible outcomes of the game are as follows: Determine in a convincing way if A and C are statistically independent.

Solution

as you can see the sum of all probabilities is 1

1/3 + 1/6 + 1/6 + 1/3 =1

they are independent because as you can see in the first trial you can take A or B

and the second trial you can take C or D

if you take C is independent of A , the second trail can be C independently if the first trial you outcome A or B