Question: A message consists of a string of bits (0s and 1s). Due to noise in the communication channel, each bit has probability 0.25 of being reversed. To improve the accuracy of the communication, each bit is sent three times (000). The receiver assigns the value 0 if two or more of the bits are decoded as 0, and 1 otherwise. Assume that errors occur independently.

1. A 0 is sent (as 000). What is the probability that the receiver assigns the correct value of 0?
2. Assume that each bit is sent n times, where n is an odd number, and that the receiver assigns the value decoded in the majority of the bits. What is the number of n necessary so that the probability that the correct value is assigned is at least 0.99?

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