GATE 2022 EC – Question 62

Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with probability $(1-\epsilon)$, and flipped with probability $\epsilon$. For each codeword transmission, the receiver performs minimum Hamming distance decoding, and correctly decodes the message bits if and only if the channel introduces at most one bit error.

For $\epsilon=0.1$, the probability that a transmitted codeword is decoded correctly is ________ (rounded off to two decimal places).