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Appending three extra (binary) bits to a 4-bit word in a particular way (a Hamming Code) allows detection and correction of up to 1 error in any of the bits. If each bit has a probability of .05 of being changed during the communication, and if the bits are changed independently of each other, what is the probability that the word is correctly received (that is, 0 or 1 bit is in error)? How does this probability compare to the probability that the word will be received correctly if we didn't use check bits, in which case all 4 bits would have to be received correctly for the word to be correct?

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