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Mathematics, 31.12.2021 14:00 david1236544

Two three-letter strings, aaa and bbb, are transmitted electronically. Each string is sent letter by letter. Due to faulty equipment, each of the six letters has a 1/3 chance of being received incorrectly, as an a when it should have been a b, or as a b when it should be an a. However, whether a given letter is received correctly or incorrectly is independent of the reception of any other letter. Let Sa be the three-letter string received when aaa is transmitted and let Sb be the three-letter string received when bbb is transmitted. Find the probability that Sa comes before Sb in alphabetical order.

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