A binary symmetric channel has reliability p.
(a) What is the minimum value of p allowable, if there is to be at least a 95% chance of no errors at all in the transmission of a binary word of length 15?
(b) Give the inequality that p must satisfy if there is to be at least a 95% chance of no more than one error in the transmission of a binary word of length 15. For the numerically deft and/or curious: is the minimum value of p satisfying this requirement significantly less than the minimum p satisfying the more stringent requirement in part (a)?
(c) What is the minimum value of p allowable if the average number of errors in transmitting binary words of length 15 is to be no greater than 1/2?