GATE Electronics and Communications (EC) 2022 Solved Paper

Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with probability(1 -ϵ), and flipped with probability ϵ. 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 ϵ = 0.1, the probability that a transmitted codeword is decoded correctly is _________ (rounded off to two decimal places).