Abstract: The precise large deviations of the sequences of the sum of random variables can accurately depict the limit state of tail probability，and in many fields have important researching and using value. This paper studies the precise large deviations of the sum of random variables with the long tail in the binary weighted dependent model，and obtains two results about the non-random weighted sum S_n and random weighted sum S_Nt .

Key words: precise large deviation, binary weighted dependency, long tail, random variables