I need a formula to express the probability of being able to correct single digit errors in a transmitted string of digits by transmitting the string (length d) over a number (n) of independent links in parallel assuming that each link has probability (p) of getting one random digit wrong. This is just for a 'toy' explanation of how to exploit redundant links for error correction.

I half-remember the basics of probability theory but I'd be grateful if comeone could guide me to a formula or a subject area that is applicable to this problem. As an example it seems to me tht if you ask 5 people to remember a 7-digit phone number and each of them gets one random digit wrong, you can correct most errors by taking a 'majority vote' on each digit, but you also have to allow for the probability that several people may 'invent' the same digit and thus win the majority vote and reduce the proportion of errors that can be corrected. What formula can you use to decide how many people you need to achieve say 98% correction of single digit errors?