What is the probability of breaking the AES algorithm?

I am doing a project which requires the encryption to be done using AES. Is it really possible (technically) to crack AES?

If yes, please tell me:

• What is the probability of breaking AES?
• How does the round number influence this probability? Do more rounds really help in decreasing this probability?
• What is the contribution of each round towards enhancing the security?
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Please note that a block cipher can be used with several modes of execution. A few examples : ECB (Electronic CodeBook), CBC (Cipher Block Chaining), CTR (CounTeR mode) ... In addition to the AES security itself, the mode you pick up can also have some specific security concerns. –  Rerito Mar 27 '13 at 12:59

The probability of breaking AES using this method? AES has 128, 192 and 256 bit key variants. Thus if there are $n$ bits in the key, the probability that your guess is correct is $\frac{1}{2^n}$.
There would be practical attacks against reduced-round AES; e.g. this, claiming an attack against 4 rounds with 4 chosen plaintext using $2^{32}$ effort and moderate memory. Theoretical attacks exist for more rounds, e.g this. Difficulty of attack increases "quickly" with the number of rounds, but it is hard to quantitatively characterize. –  fgrieu Mar 26 '13 at 12:36