Independent events (for three events)

For example, if we roll a dice twice.
First event is getting a 3 in the first roll. (A)
Second event is getting a 4 in the second roll. (B)
Third event is getting 7 for total two rolls. (C)
How can we determine all three events are independent?

p(A) = 1/6
p(B) = 1/6
p(c) = (3,4)(4,3)(2,5)(5,2)(1,6)(6,1)
= 6/36
= 1/6

p(AB) = p(A)p(B)
? = 1/36

i'm not sure how to find the left side, p(AB).
same for the below parts.

p(AC) = p(A)p(C)
p(BC) = p(B)p(C)

p(ABC) = p(A)p(B)p(C)
? = (1/6)^3
= 1/216 -----> is this correct?

any help,please.
thanks!

Your question leaves me wondering what the situation truly is.

>For example, if we roll a dice twice.
First event is getting a 3 in the first roll. (A)
Second event is getting a 4 in the second roll. (B)
Third event is getting 7 for total two rolls. (C)

The word "dice" is plural. Do you mean "roll a die twice" or are you rolling more than one?
If you roll a die twice, it is my understanding that you have two events. I don't understand the "third event". Maybe you mean the "outcome".
Your question "How can we determine all three events are independent?" also leaves me wondering. I believe that you determine whether or not events are independent or dependent based on the circumstances. For me to decide in this particular case, I would ask myself "does the die remember the result of the first event and try to duplicate this or avoid duplicating it?" If I thought the outcome of the second event depended on the outcome of the first event, then I would determine that the two events were dependent. Otherwise they are independent.

i'm sorry if my understanding of the question that makes it hard to understand.

the original question is,

consider rolling a die twice. Let A be the event that the first roll is a 3. Let B be the event that the second roll is a 4 and let C be the event that the total of the two rolls is 7. Are A, B and C independent events?

how can we justify that?

In reading the question, I at first assumed that all three events were either dependent or independent. Then, I noted that the word "all" is not included. If I were to answer the question, I would indicate that I think the three events are not all the same, regarding being dependent or independent. I would then explain what I think each event is (dependent or independent) and why I think that.