Dice Rolling: Stuck in the middle of question that instantly come into my mind

[Dr.Peterson]

OP said that s/he was looking for a "match" that was "the same"- which I took to mean that they were looking for a particular number.

There are 2 pieces of 6 sided dice we have. We roll them 5 times one after another. What is the probability that the numbers on the front side are same (same numbers) at least one times of 5 turns?

I don't see the word "match" there; but what it says is that the numbers are the same. There is no mention of any number having been chosen that they are the same as.

But this is why questions in probability have to be stated very carefully, and often we need to ask for clarification, perhaps proposing a carefully worded paraphrase to make sure our interpretation is what was intended - all the more so when the question might be translated into English by someone who doesn't speak English well. (That can include native English speakers, more than you might think.)

It's also important, then, to look at other things the OP has said that might clarify the intent. And that is clear here:

1st dice could be any number (6/6)
2nd dice have to be same number with 1st dice(1/6)

Then result for the problem is (6/6).(1/6)=1/6

This makes it very clear! This is correct work, and nicely shows what the problem means to the OP.

I say all this not to put you down, but to illustrate some important aspects of answering a question carefully.

 

[Selim47]

OP said that s/he was looking for a "match" that was "the same"- which I took to mean that they were looking for a particular number.

To be honest, all the confusion has been arisen due to my lack of English. I'm sorry about that

 

[Dr.Peterson]

To be honest, all the confusion has been arisen due to my lack of English. I'm sorry about that

No, it's our fault for responding to it inadequately. Your math is far better than your English, and that's what counts. All of us need to learn to communicate better ...

I often advise students whose English is not good to simply say more, rather than less (as they often want to) -- to express things in more than one way, so that together they will be clearer than any one phrase would be. This is called redundancy, and it is a good thing in communication. You have done exactly that, and have done it well. Thanks for doing your part!