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A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times ($0$ is transmitted as $000$, and $1$ is transmitted as $111$). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three received bits, if the number of zeroes exceeds the number of ones, the decoder decides in favor of a $0$, and if the number of ones exceeds the number of zeroes, the decoder decides in favor of a $1$. Assuming a binary symmetric channel with crossover probability $p=0.1$, the average probability of error is _________
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