A certain type of Hamming code adds 3 bits to every 4-bit word. With this extra information, any single bit transmission error can be detected and corrected. Suppose a signal is sent over a poor channel where the probability is 0.05 that any given bit will be incorrectly received (a 0 sent but a 1 received or vice versa) and that errors are independent.
a) What is the probability that an encoded 4-bit word will be correctly interpreted by the receiver?
b) What is the probability that a Hamming-coded 4-bit word (7 total bits) will be correctly interpreted by the receiver?
c) Make a graph that shows how the probability of correct interpretation depends on the bitwise error rate in each situation.