Consider a binary communication channel with an error probability of p$=0\mathrm{.}01.$ Assume that if n bits are transmitted, the errors occur independently in each of the n bits. Now consider an error control code, which adds $3$ parity bits to $4$ information bits. Such a code can correct one error in the $7$ bits that are sent. What is the error probability in one $4-$bit word without the error correcting code and with the error correcting code