A computer communication channel transmits words of n bits using an error-correcting code which is capable of correcting errors in up to k bits. Here each bit is either a 0 or a 1. Assume each bit is transmitted correctly with probability p and incorrectly with probability q independently of all other bits.
a) Find a formula for the probability that a word is correctly transmitted.
b) Calculate the probability of correct transmission for n = 8, k = 2, and q = = 0.01.