Then, next to each word which is transmitted, another parity digit is placed such that the total number of 1’s representing a word is an even integer. When the word with the n + 1 digits is transmitted to the receiver, this receiver checks the number of 1’s received and if this is not an even number,

it reports an error in the data transportation. Suppose that each digit is transmitted correctly with probability p (0 < p < 1).
(i) Find the distribution of the number X of digits that are correctly transmitted.
(ii) What is the probability that a word which is not transmitted correctly passes unnoticed?
(iii) Give numerical answers to the previous two parts for p = 0.98 when n = 3 and n = 6.